diff --git a/CHANGES b/CHANGES
index 934c553e3..33cc8ccf7 100644
--- a/CHANGES
+++ b/CHANGES
@@ -7,6 +7,8 @@ Dependencies
 Incompatible changes
 --------------------
 
+* Drop features and APIs deprecated in 1.8.x
+
 Deprecated
 ----------
 
diff --git a/doc/extdev/appapi.rst b/doc/extdev/appapi.rst
index fe64628a4..4cb8501be 100644
--- a/doc/extdev/appapi.rst
+++ b/doc/extdev/appapi.rst
@@ -54,8 +54,6 @@ package.
 
 .. automethod:: Sphinx.add_domain(domain)
 
-.. automethod:: Sphinx.override_domain(domain)
-
 .. method:: Sphinx.add_directive_to_domain(domain, name, func, content, arguments, \*\*options)
 .. automethod:: Sphinx.add_directive_to_domain(domain, name, directiveclass)
 
diff --git a/sphinx/addnodes.py b/sphinx/addnodes.py
index ef3bf3f9e..4180625ca 100644
--- a/sphinx/addnodes.py
+++ b/sphinx/addnodes.py
@@ -12,7 +12,7 @@ import warnings
 
 from docutils import nodes
 
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 
 if False:
     # For type annotation
@@ -188,59 +188,6 @@ class production(nodes.Part, nodes.Inline, nodes.FixedTextElement):
     """Node for a single grammar production rule."""
 
 
-# math nodes
-
-
-class math(nodes.math):
-    """Node for inline equations.
-
-    .. warning:: This node is provided to keep compatibility only.
-                 It will be removed in nearly future.  Don't use this from your extension.
-
-    .. deprecated:: 1.8
-       Use ``docutils.nodes.math`` instead.
-    """
-
-    def __getitem__(self, key):
-        """Special accessor for supporting ``node['latex']``."""
-        if key == 'latex' and 'latex' not in self.attributes:
-            warnings.warn("math node for Sphinx was replaced by docutils'. "
-                          "Therefore please use ``node.astext()`` to get an equation instead.",
-                          RemovedInSphinx30Warning, stacklevel=2)
-            return self.astext()
-        else:
-            return super().__getitem__(key)
-
-
-class math_block(nodes.math_block):
-    """Node for block level equations.
-
-    .. warning:: This node is provided to keep compatibility only.
-                 It will be removed in nearly future.  Don't use this from your extension.
-
-    .. deprecated:: 1.8
-    """
-
-    def __getitem__(self, key):
-        if key == 'latex' and 'latex' not in self.attributes:
-            warnings.warn("displaymath node for Sphinx was replaced by docutils'. "
-                          "Therefore please use ``node.astext()`` to get an equation instead.",
-                          RemovedInSphinx30Warning, stacklevel=2)
-            return self.astext()
-        else:
-            return super().__getitem__(key)
-
-
-class displaymath(math_block):
-    """Node for block level equations.
-
-    .. warning:: This node is provided to keep compatibility only.
-                 It will be removed in nearly future.  Don't use this from your extension.
-
-    .. deprecated:: 1.8
-    """
-
-
 # other directive-level nodes
 
 class index(nodes.Invisible, nodes.Inline, nodes.TextElement):
@@ -379,7 +326,6 @@ def setup(app):
     app.add_node(seealso)
     app.add_node(productionlist)
     app.add_node(production)
-    app.add_node(displaymath)
     app.add_node(index)
     app.add_node(centered)
     app.add_node(acks)
diff --git a/sphinx/application.py b/sphinx/application.py
index aee9f4410..516b7be58 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -15,7 +15,6 @@ import pickle
 import sys
 import warnings
 from collections import deque
-from inspect import isclass
 from io import StringIO
 from os import path
 
@@ -25,9 +24,7 @@ import sphinx
 from sphinx import package_dir, locale
 from sphinx.config import Config
 from sphinx.config import CONFIG_FILENAME  # NOQA # for compatibility (RemovedInSphinx30)
-from sphinx.deprecation import (
-    RemovedInSphinx30Warning, RemovedInSphinx40Warning
-)
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.environment import BuildEnvironment
 from sphinx.errors import ApplicationError, ConfigError, VersionRequirementError
 from sphinx.events import EventManager
@@ -35,11 +32,10 @@ from sphinx.locale import __
 from sphinx.project import Project
 from sphinx.registry import SphinxComponentRegistry
 from sphinx.util import docutils
-from sphinx.util import import_object, progress_message
 from sphinx.util import logging
+from sphinx.util import progress_message
 from sphinx.util.build_phase import BuildPhase
 from sphinx.util.console import bold  # type: ignore
-from sphinx.util.docutils import directive_helper
 from sphinx.util.i18n import CatalogRepository
 from sphinx.util.logging import prefixed_warnings
 from sphinx.util.osutil import abspath, ensuredir, relpath
@@ -98,7 +94,6 @@ builtin_extensions = (
     'sphinx.transforms.post_transforms',
     'sphinx.transforms.post_transforms.code',
     'sphinx.transforms.post_transforms.images',
-    'sphinx.transforms.post_transforms.compat',
     'sphinx.util.compat',
     'sphinx.versioning',
     # collectors should be loaded by specific order
@@ -397,18 +392,6 @@ class Sphinx:
         if version > sphinx.__display_version__[:3]:
             raise VersionRequirementError(version)
 
-    def import_object(self, objname, source=None):
-        # type: (str, str) -> Any
-        """Import an object from a ``module.name`` string.
-
-        .. deprecated:: 1.8
-           Use ``sphinx.util.import_object()`` instead.
-        """
-        warnings.warn('app.import_object() is deprecated. '
-                      'Use sphinx.util.add_object_type() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return import_object(objname, source=None)
-
     # event interface
     def connect(self, event, callback):
         # type: (str, Callable) -> int
@@ -593,36 +576,14 @@ class Sphinx:
         self.registry.add_enumerable_node(node, figtype, title_getter, override=override)
         self.add_node(node, override=override, **kwds)
 
-    @property
-    def enumerable_nodes(self):
-        # type: () -> Dict[Type[nodes.Node], Tuple[str, TitleGetter]]
-        warnings.warn('app.enumerable_nodes() is deprecated. '
-                      'Use app.get_domain("std").enumerable_nodes instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.registry.enumerable_nodes
-
-    def add_directive(self, name, obj, content=None, arguments=None, override=False, **options):  # NOQA
-        # type: (str, Any, bool, Tuple[int, int, bool], bool, Any) -> None
+    def add_directive(self, name, cls, override=False):
+        # type: (str, Type[Directive], bool) -> None
         """Register a Docutils directive.
 
-        *name* must be the prospective directive name.  There are two possible
-        ways to write a directive:
-
-        - In the docutils 0.4 style, *obj* is the directive function.
-          *content*, *arguments* and *options* are set as attributes on the
-          function and determine whether the directive has content, arguments
-          and options, respectively.  **This style is deprecated.**
-
-        - In the docutils 0.5 style, *obj* is the directive class.
-          It must already have attributes named *has_content*,
-          *required_arguments*, *optional_arguments*,
-          *final_argument_whitespace* and *option_spec* that correspond to the
-          options for the function way.  See `the Docutils docs
-          <http://docutils.sourceforge.net/docs/howto/rst-directives.html>`_
-          for details.
-
-        The directive class must inherit from the class
-        ``docutils.parsers.rst.Directive``.
+        *name* must be the prospective directive name.  *cls* is a directive
+        class which inherits ``docutils.parsers.rst.Directive``.  For more
+        details, see `the Docutils docs
+        <http://docutils.sourceforge.net/docs/howto/rst-directives.html>`_ .
 
         For example, the (already existing) :rst:dir:`literalinclude` directive
         would be added like this:
@@ -653,17 +614,12 @@ class Sphinx:
         .. versionchanged:: 1.8
            Add *override* keyword.
         """
-        logger.debug('[app] adding directive: %r',
-                     (name, obj, content, arguments, options))
+        logger.debug('[app] adding directive: %r', (name, cls))
         if not override and docutils.is_directive_registered(name):
             logger.warning(__('directive %r is already registered, it will be overridden'),
                            name, type='app', subtype='add_directive')
 
-        if not isclass(obj) or not issubclass(obj, Directive):
-            directive = directive_helper(obj, content, arguments, **options)
-            docutils.register_directive(name, directive)
-        else:
-            docutils.register_directive(name, obj)
+        docutils.register_directive(name, cls)
 
     def add_role(self, name, role, override=False):
         # type: (str, Any, bool) -> None
@@ -716,26 +672,8 @@ class Sphinx:
         """
         self.registry.add_domain(domain, override=override)
 
-    def override_domain(self, domain):
-        # type: (Type[Domain]) -> None
-        """Override a registered domain.
-
-        Make the given *domain* class known to Sphinx, assuming that there is
-        already a domain with its ``.name``.  The new domain must be a subclass
-        of the existing one.
-
-        .. versionadded:: 1.0
-        .. deprecated:: 1.8
-           Integrated to :meth:`add_domain`.
-        """
-        warnings.warn('app.override_domain() is deprecated. '
-                      'Use app.add_domain() with override option instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        self.registry.add_domain(domain, override=True)
-
-    def add_directive_to_domain(self, domain, name, obj, has_content=None, argument_spec=None,
-                                override=False, **option_spec):
-        # type: (str, str, Any, bool, Any, bool, Any) -> None
+    def add_directive_to_domain(self, domain, name, cls, override=False):
+        # type: (str, str, Type[Directive], bool) -> None
         """Register a Docutils directive in a domain.
 
         Like :meth:`add_directive`, but the directive is added to the domain
@@ -745,9 +683,7 @@ class Sphinx:
         .. versionchanged:: 1.8
            Add *override* keyword.
         """
-        self.registry.add_directive_to_domain(domain, name, obj,
-                                              has_content, argument_spec, override=override,
-                                              **option_spec)
+        self.registry.add_directive_to_domain(domain, name, cls, override=override)
 
     def add_role_to_domain(self, domain, name, role, override=False):
         # type: (str, str, Union[RoleFunction, XRefRole], bool) -> None
@@ -1205,13 +1141,6 @@ class Sphinx:
 
         return True
 
-    @property
-    def _setting_up_extension(self):
-        # type: () -> List[str]
-        warnings.warn('app._setting_up_extension is deprecated.',
-                      RemovedInSphinx30Warning)
-        return ['?']
-
 
 class TemplateBridge:
     """
diff --git a/sphinx/builders/html.py b/sphinx/builders/html.py
index 3f167d0d3..5621f9a75 100644
--- a/sphinx/builders/html.py
+++ b/sphinx/builders/html.py
@@ -24,9 +24,7 @@ from docutils.utils import relative_path
 
 from sphinx import package_dir, __display_version__
 from sphinx.builders import Builder
-from sphinx.deprecation import (
-    RemovedInSphinx30Warning, RemovedInSphinx40Warning, deprecated_alias
-)
+from sphinx.deprecation import RemovedInSphinx40Warning, deprecated_alias
 from sphinx.environment.adapters.asset import ImageAdapter
 from sphinx.environment.adapters.indexentries import IndexEntries
 from sphinx.environment.adapters.toctree import TocTree
@@ -105,39 +103,6 @@ class Stylesheet(str):
         return self
 
 
-class JSContainer(list):
-    """The container for JavaScript scripts."""
-    def insert(self, index, obj):
-        # type: (int, str) -> None
-        warnings.warn('To modify script_files in the theme is deprecated. '
-                      'Please insert a <script> tag directly in your theme instead.',
-                      RemovedInSphinx30Warning, stacklevel=3)
-        super().insert(index, obj)
-
-    def extend(self, other):  # type: ignore
-        # type: (List[str]) -> None
-        warnings.warn('To modify script_files in the theme is deprecated. '
-                      'Please insert a <script> tag directly in your theme instead.',
-                      RemovedInSphinx30Warning, stacklevel=3)
-        for item in other:
-            self.append(item)
-
-    def __iadd__(self, other):  # type: ignore
-        # type: (List[str]) -> JSContainer
-        warnings.warn('To modify script_files in the theme is deprecated. '
-                      'Please insert a <script> tag directly in your theme instead.',
-                      RemovedInSphinx30Warning, stacklevel=3)
-        for item in other:
-            self.append(item)
-        return self
-
-    def __add__(self, other):
-        # type: (List[str]) -> JSContainer
-        ret = JSContainer(self)
-        ret += other
-        return ret
-
-
 class JavaScript(str):
     """A metadata of javascript file.
 
@@ -247,7 +212,7 @@ class StandaloneHTMLBuilder(Builder):
         self.css_files = []  # type: List[Dict[str, str]]
 
         # JS files
-        self.script_files = JSContainer()  # type: List[JavaScript]
+        self.script_files = []  # type: List[JavaScript]
 
     def init(self):
         # type: () -> None
@@ -1068,16 +1033,6 @@ class StandaloneHTMLBuilder(Builder):
             return False
         ctx['hasdoc'] = hasdoc
 
-        def warn(*args, **kwargs):
-            # type: (Any, Any) -> str
-            """Simple warn() wrapper for themes."""
-            warnings.warn('The template function warn() was deprecated. '
-                          'Use warning() instead.',
-                          RemovedInSphinx30Warning, stacklevel=2)
-            logger.warning(*args, **kwargs)
-            return ''  # return empty string
-        ctx['warn'] = warn
-
         ctx['toctree'] = lambda **kw: self._get_local_toctree(pagename, **kw)
         self.add_sidebars(pagename, ctx)
         ctx.update(addctx)
diff --git a/sphinx/builders/latex/util.py b/sphinx/builders/latex/util.py
index 156ea89ad..1765cb0ce 100644
--- a/sphinx/builders/latex/util.py
+++ b/sphinx/builders/latex/util.py
@@ -8,12 +8,8 @@
     :license: BSD, see LICENSE for details.
 """
 
-import warnings
-
 from docutils.writers.latex2e import Babel
 
-from sphinx.deprecation import RemovedInSphinx30Warning
-
 
 class ExtBabel(Babel):
     cyrillic_languages = ('bulgarian', 'kazakh', 'mongolian', 'russian', 'ukrainian')
@@ -25,13 +21,6 @@ class ExtBabel(Babel):
         self.supported = True
         super().__init__(language_code or '')
 
-    def get_shorthandoff(self):
-        # type: () -> str
-        warnings.warn('ExtBabel.get_shorthandoff() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        from sphinx.writers.latex import SHORTHANDOFF
-        return SHORTHANDOFF
-
     def uses_cyrillic(self):
         # type: () -> bool
         return self.language in self.cyrillic_languages
diff --git a/sphinx/cmdline.py b/sphinx/cmdline.py
deleted file mode 100644
index 5247eb157..000000000
--- a/sphinx/cmdline.py
+++ /dev/null
@@ -1,49 +0,0 @@
-"""
-    sphinx.cmdline
-    ~~~~~~~~~~~~~~
-
-    sphinx-build command-line handling.
-
-    :copyright: Copyright 2007-2019 by the Sphinx team, see AUTHORS.
-    :license: BSD, see LICENSE for details.
-"""
-
-import sys
-import warnings
-
-from sphinx.cmd import build
-from sphinx.deprecation import RemovedInSphinx30Warning
-
-if False:
-    # For type annotation
-    import argparse  # NOQA
-    from typing import Any, IO, List, Union  # NOQA
-    from sphinx.application import Sphinx  # NOQA
-
-
-def handle_exception(app, args, exception, stderr=sys.stderr):
-    # type: (Sphinx, Any, Union[Exception, KeyboardInterrupt], IO) -> None
-    warnings.warn('sphinx.cmdline module is deprecated. Use sphinx.cmd.build instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    build.handle_exception(app, args, exception, stderr)
-
-
-def jobs_argument(value):
-    # type: (str) -> int
-    warnings.warn('sphinx.cmdline module is deprecated. Use sphinx.cmd.build instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return build.jobs_argument(value)
-
-
-def get_parser():
-    # type: () -> argparse.ArgumentParser
-    warnings.warn('sphinx.cmdline module is deprecated. Use sphinx.cmd.build instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return build.get_parser()
-
-
-def main(argv=sys.argv[1:]):
-    # type: (List[str]) -> int
-    warnings.warn('sphinx.cmdline module is deprecated. Use sphinx.cmd.build instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return build.main(argv)
diff --git a/sphinx/config.py b/sphinx/config.py
index 5ba2c2a3d..06718eb2b 100644
--- a/sphinx/config.py
+++ b/sphinx/config.py
@@ -16,7 +16,7 @@ from collections import OrderedDict
 from os import path, getenv
 from typing import Any, NamedTuple, Union
 
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.errors import ConfigError, ExtensionError
 from sphinx.locale import _, __
 from sphinx.util import logging
@@ -155,27 +155,8 @@ class Config:
                                  'env', []),
     }  # type: Dict[str, Tuple]
 
-    def __init__(self, *args):
-        # type: (Any) -> None
-        if len(args) == 4:
-            # old style arguments: (dirname, filename, overrides, tags)
-            warnings.warn('The argument of Config() class has been changed. '
-                          'Use Config.read() to read configuration from conf.py.',
-                          RemovedInSphinx30Warning, stacklevel=2)
-            dirname, filename, overrides, tags = args
-            if dirname is None:
-                config = {}  # type: Dict[str, Any]
-            else:
-                config = eval_config_file(path.join(dirname, filename), tags)
-        else:
-            # new style arguments: (config={}, overrides={})
-            if len(args) == 0:
-                config, overrides = {}, {}
-            elif len(args) == 1:
-                config, overrides = args[0], {}
-            else:
-                config, overrides = args[:2]
-
+    def __init__(self, config={}, overrides={}):
+        # type: (Dict[str, Any], Dict[str, Any]) -> None
         self.overrides = overrides
         self.values = Config.config_values.copy()
         self._raw_config = config
@@ -196,18 +177,6 @@ class Config:
         namespace = eval_config_file(filename, tags)
         return cls(namespace, overrides or {})
 
-    def check_types(self):
-        # type: () -> None
-        warnings.warn('Config.check_types() is deprecated. Use check_confval_types() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        check_confval_types(None, self)
-
-    def check_unicode(self):
-        # type: () -> None
-        warnings.warn('Config.check_unicode() is deprecated. Use check_unicode() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        check_unicode(self)
-
     def convert_overrides(self, name, value):
         # type: (str, Any) -> Any
         if not isinstance(value, str):
diff --git a/sphinx/deprecation.py b/sphinx/deprecation.py
index 6cdd22ec1..1169280d0 100644
--- a/sphinx/deprecation.py
+++ b/sphinx/deprecation.py
@@ -17,15 +17,11 @@ if False:
     from typing import Any, Dict, Type  # NOQA
 
 
-class RemovedInSphinx30Warning(PendingDeprecationWarning):
-    pass
-
-
 class RemovedInSphinx40Warning(PendingDeprecationWarning):
     pass
 
 
-RemovedInNextVersionWarning = RemovedInSphinx30Warning
+RemovedInNextVersionWarning = RemovedInSphinx40Warning
 
 
 def deprecated_alias(modname, objects, warning):
diff --git a/sphinx/domains/changeset.py b/sphinx/domains/changeset.py
index aeea645c1..d731fe183 100644
--- a/sphinx/domains/changeset.py
+++ b/sphinx/domains/changeset.py
@@ -14,8 +14,6 @@ from typing import cast
 from docutils import nodes
 
 from sphinx import addnodes
-from sphinx import locale
-from sphinx.deprecation import DeprecatedDict, RemovedInSphinx30Warning
 from sphinx.domains import Domain
 from sphinx.locale import _
 from sphinx.util.docutils import SphinxDirective
@@ -40,13 +38,6 @@ versionlabel_classes = {
     'deprecated':       'deprecated',
 }
 
-locale.versionlabels = DeprecatedDict(
-    versionlabels,
-    'sphinx.locale.versionlabels is deprecated. '
-    'Please use sphinx.domains.changeset.versionlabels instead.',
-    RemovedInSphinx30Warning
-)
-
 
 # TODO: move to typing.NamedTuple after dropping py35 support (see #5958)
 ChangeSet = namedtuple('ChangeSet',
diff --git a/sphinx/domains/math.py b/sphinx/domains/math.py
index bc0ef8328..be5838794 100644
--- a/sphinx/domains/math.py
+++ b/sphinx/domains/math.py
@@ -11,7 +11,6 @@
 from docutils import nodes
 from docutils.nodes import make_id
 
-from sphinx.addnodes import math_block as displaymath
 from sphinx.domains import Domain
 from sphinx.locale import __
 from sphinx.roles import XRefRole
@@ -49,7 +48,6 @@ class MathDomain(Domain):
         'eq': 'equation not found: %(target)s',
     }
     enumerable_nodes = {  # node_class -> (figtype, title_getter)
-        displaymath: ('displaymath', None),
         nodes.math_block: ('displaymath', None),
     }
     roles = {
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index ea71aa976..2203ee6e3 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -13,8 +13,7 @@ import re
 from docutils import nodes
 from docutils.parsers.rst import directives
 
-from sphinx import addnodes, locale
-from sphinx.deprecation import DeprecatedDict, RemovedInSphinx30Warning
+from sphinx import addnodes
 from sphinx.directives import ObjectDescription
 from sphinx.domains import Domain, ObjType, Index, IndexEntry
 from sphinx.locale import _, __
@@ -55,13 +54,6 @@ pairindextypes = {
     'builtin':   _('built-in function'),
 }
 
-locale.pairindextypes = DeprecatedDict(
-    pairindextypes,
-    'sphinx.locale.pairindextypes is deprecated. '
-    'Please use sphinx.domains.python.pairindextypes instead.',
-    RemovedInSphinx30Warning
-)
-
 
 def _pseudo_parse_arglist(signode, arglist):
     # type: (addnodes.desc_signature, str) -> None
diff --git a/sphinx/domains/std.py b/sphinx/domains/std.py
index 04e8219c4..e73c660e6 100644
--- a/sphinx/domains/std.py
+++ b/sphinx/domains/std.py
@@ -10,7 +10,6 @@
 
 import re
 import unicodedata
-import warnings
 from copy import copy
 from typing import cast
 
@@ -19,7 +18,6 @@ from docutils.parsers.rst import directives
 from docutils.statemachine import StringList
 
 from sphinx import addnodes
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.directives import ObjectDescription
 from sphinx.domains import Domain, ObjType
 from sphinx.errors import NoUri
@@ -957,17 +955,6 @@ class StandardDomain(Domain):
             figtype, _ = self.enumerable_nodes.get(node.__class__, (None, None))
             return figtype
 
-    def get_figtype(self, node):
-        # type: (nodes.Node) -> str
-        """Get figure type of nodes.
-
-        .. deprecated:: 1.8
-        """
-        warnings.warn('StandardDomain.get_figtype() is deprecated. '
-                      'Please use get_enumerable_node_type() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.get_enumerable_node_type(node)
-
     def get_fignumber(self, env, builder, figtype, docname, target_node):
         # type: (BuildEnvironment, Builder, str, str, nodes.Element) -> Tuple[int, ...]
         if figtype == 'section':
diff --git a/sphinx/environment/__init__.py b/sphinx/environment/__init__.py
index e3d2c1f49..f931b3b13 100644
--- a/sphinx/environment/__init__.py
+++ b/sphinx/environment/__init__.py
@@ -13,13 +13,10 @@ import pickle
 import warnings
 from collections import defaultdict
 from copy import copy
-from io import BytesIO
 from os import path
 
 from sphinx import addnodes
-from sphinx.deprecation import (
-    RemovedInSphinx30Warning, RemovedInSphinx40Warning, deprecated_alias
-)
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.environment.adapters.toctree import TocTree
 from sphinx.errors import SphinxError, BuildEnvironmentError, DocumentError, ExtensionError
 from sphinx.locale import __
@@ -657,133 +654,3 @@ class BuildEnvironment:
         for domain in self.domains.values():
             domain.check_consistency()
         self.app.emit('env-check-consistency', self)
-
-    # --------- METHODS FOR COMPATIBILITY --------------------------------------
-
-    def update(self, config, srcdir, doctreedir):
-        # type: (Config, str, str) -> List[str]
-        warnings.warn('env.update() is deprecated. Please use builder.read() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.app.builder.read()
-
-    def _read_serial(self, docnames, app):
-        # type: (List[str], Sphinx) -> None
-        warnings.warn('env._read_serial() is deprecated. Please use builder.read() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.app.builder._read_serial(docnames)
-
-    def _read_parallel(self, docnames, app, nproc):
-        # type: (List[str], Sphinx, int) -> None
-        warnings.warn('env._read_parallel() is deprecated. Please use builder.read() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.app.builder._read_parallel(docnames, nproc)
-
-    def read_doc(self, docname, app=None):
-        # type: (str, Sphinx) -> None
-        warnings.warn('env.read_doc() is deprecated. Please use builder.read_doc() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        self.app.builder.read_doc(docname)
-
-    def write_doctree(self, docname, doctree):
-        # type: (str, nodes.document) -> None
-        warnings.warn('env.write_doctree() is deprecated. '
-                      'Please use builder.write_doctree() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        self.app.builder.write_doctree(docname, doctree)
-
-    @property
-    def _nitpick_ignore(self):
-        # type: () -> List[str]
-        warnings.warn('env._nitpick_ignore is deprecated. '
-                      'Please use config.nitpick_ignore instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.config.nitpick_ignore
-
-    @staticmethod
-    def load(f, app=None):
-        # type: (IO, Sphinx) -> BuildEnvironment
-        warnings.warn('BuildEnvironment.load() is deprecated. '
-                      'Please use pickle.load() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        try:
-            env = pickle.load(f)
-        except Exception as exc:
-            # This can happen for example when the pickle is from a
-            # different version of Sphinx.
-            raise OSError(exc)
-        if app:
-            env.app = app
-            env.config.values = app.config.values
-        return env
-
-    @classmethod
-    def loads(cls, string, app=None):
-        # type: (bytes, Sphinx) -> BuildEnvironment
-        warnings.warn('BuildEnvironment.loads() is deprecated. '
-                      'Please use pickle.loads() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        io = BytesIO(string)
-        return cls.load(io, app)
-
-    @classmethod
-    def frompickle(cls, filename, app):
-        # type: (str, Sphinx) -> BuildEnvironment
-        warnings.warn('BuildEnvironment.frompickle() is deprecated. '
-                      'Please use pickle.load() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        with open(filename, 'rb') as f:
-            return cls.load(f, app)
-
-    @staticmethod
-    def dump(env, f):
-        # type: (BuildEnvironment, IO) -> None
-        warnings.warn('BuildEnvironment.dump() is deprecated. '
-                      'Please use pickle.dump() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        pickle.dump(env, f, pickle.HIGHEST_PROTOCOL)
-
-    @classmethod
-    def dumps(cls, env):
-        # type: (BuildEnvironment) -> bytes
-        warnings.warn('BuildEnvironment.dumps() is deprecated. '
-                      'Please use pickle.dumps() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        io = BytesIO()
-        cls.dump(env, io)
-        return io.getvalue()
-
-    def topickle(self, filename):
-        # type: (str) -> None
-        warnings.warn('env.topickle() is deprecated. '
-                      'Please use pickle.dump() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        with open(filename, 'wb') as f:
-            self.dump(self, f)
-
-    @property
-    def versionchanges(self):
-        # type: () -> Dict[str, List[Tuple[str, str, int, str, str, str]]]
-        warnings.warn('env.versionchanges() is deprecated. '
-                      'Please use ChangeSetDomain instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.domaindata['changeset']['changes']
-
-    def note_versionchange(self, type, version, node, lineno):
-        # type: (str, str, addnodes.versionmodified, int) -> None
-        warnings.warn('env.note_versionchange() is deprecated. '
-                      'Please use ChangeSetDomain.note_changeset() instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        node['type'] = type
-        node['version'] = version
-        node.line = lineno
-        self.get_domain('changeset').note_changeset(node)  # type: ignore
-
-
-from sphinx.errors import NoUri  # NOQA
-
-
-deprecated_alias('sphinx.environment',
-                 {
-                     'NoUri': NoUri,
-                 },
-                 RemovedInSphinx30Warning)
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 5d96affa4..8446ab66b 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -18,9 +18,7 @@ from typing import Any
 from docutils.statemachine import StringList
 
 import sphinx
-from sphinx.deprecation import (
-    RemovedInSphinx30Warning, RemovedInSphinx40Warning, deprecated_alias
-)
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.ext.autodoc.importer import import_object, get_object_members
 from sphinx.ext.autodoc.mock import mock
 from sphinx.locale import _, __
@@ -1448,39 +1446,6 @@ def autodoc_attrgetter(app, obj, name, *defargs):
     return safe_getattr(obj, name, *defargs)
 
 
-def merge_autodoc_default_flags(app, config):
-    # type: (Sphinx, Config) -> None
-    """This merges the autodoc_default_flags to autodoc_default_options."""
-    if not config.autodoc_default_flags:
-        return
-
-    # Note: this option will be removed in Sphinx-4.0.  But I marked this as
-    # RemovedInSphinx *30* Warning because we have to emit warnings for users
-    # who will be still in use with Sphinx-3.x.  So we should replace this by
-    # logger.warning() on 3.0.0 release.
-    warnings.warn('autodoc_default_flags is now deprecated. '
-                  'Please use autodoc_default_options instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-
-    for option in config.autodoc_default_flags:
-        if isinstance(option, str):
-            config.autodoc_default_options[option] = None
-        else:
-            logger.warning(
-                __("Ignoring invalid option in autodoc_default_flags: %r"),
-                option, type='autodoc'
-            )
-
-
-from sphinx.ext.autodoc.mock import _MockImporter  # NOQA
-
-deprecated_alias('sphinx.ext.autodoc',
-                 {
-                     '_MockImporter': _MockImporter,
-                 },
-                 RemovedInSphinx40Warning)
-
-
 def setup(app):
     # type: (Sphinx) -> Dict[str, Any]
     app.add_autodocumenter(ModuleDocumenter)
@@ -1505,6 +1470,4 @@ def setup(app):
     app.add_event('autodoc-process-signature')
     app.add_event('autodoc-skip-member')
 
-    app.connect('config-inited', merge_autodoc_default_flags)
-
     return {'version': sphinx.__display_version__, 'parallel_read_safe': True}
diff --git a/sphinx/ext/autodoc/importer.py b/sphinx/ext/autodoc/importer.py
index a06d93d52..557461fd4 100644
--- a/sphinx/ext/autodoc/importer.py
+++ b/sphinx/ext/autodoc/importer.py
@@ -150,12 +150,11 @@ def get_object_members(subject, objpath, attrgetter, analyzer=None):
 
 
 from sphinx.ext.autodoc.mock import (  # NOQA
-    _MockImporter, _MockModule, _MockObject, MockFinder, MockLoader, mock
+    _MockModule, _MockObject, MockFinder, MockLoader, mock
 )
 
 deprecated_alias('sphinx.ext.autodoc.importer',
                  {
-                     '_MockImporter': _MockImporter,
                      '_MockModule': _MockModule,
                      '_MockObject': _MockObject,
                      'MockFinder': MockFinder,
diff --git a/sphinx/ext/autodoc/mock.py b/sphinx/ext/autodoc/mock.py
index 6ae389258..d896bdde2 100644
--- a/sphinx/ext/autodoc/mock.py
+++ b/sphinx/ext/autodoc/mock.py
@@ -11,12 +11,10 @@
 import contextlib
 import os
 import sys
-import warnings
 from importlib.abc import Loader, MetaPathFinder
 from importlib.machinery import ModuleSpec
 from types import FunctionType, MethodType, ModuleType
 
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.util import logging
 
 if False:
@@ -94,16 +92,12 @@ class _MockModule(ModuleType):
     """Used by autodoc_mock_imports."""
     __file__ = os.devnull
 
-    def __init__(self, name, loader=None):
-        # type: (str, _MockImporter) -> None
+    def __init__(self, name):
+        # type: (str) -> None
         super().__init__(name)
         self.__all__ = []  # type: List[str]
         self.__path__ = []  # type: List[str]
 
-        if loader is not None:
-            warnings.warn('The loader argument for _MockModule is deprecated.',
-                          RemovedInSphinx30Warning)
-
     def __getattr__(self, name):
         # type: (str) -> _MockObject
         return _make_subclass(name, self.__name__)()
@@ -113,48 +107,6 @@ class _MockModule(ModuleType):
         return self.__name__
 
 
-class _MockImporter(MetaPathFinder):
-    def __init__(self, names):
-        # type: (List[str]) -> None
-        self.names = names
-        self.mocked_modules = []  # type: List[str]
-        # enable hook by adding itself to meta_path
-        sys.meta_path.insert(0, self)
-
-        warnings.warn('_MockImporter is now deprecated.',
-                      RemovedInSphinx30Warning)
-
-    def disable(self):
-        # type: () -> None
-        # remove `self` from `sys.meta_path` to disable import hook
-        sys.meta_path = [i for i in sys.meta_path if i is not self]
-        # remove mocked modules from sys.modules to avoid side effects after
-        # running auto-documenter
-        for m in self.mocked_modules:
-            if m in sys.modules:
-                del sys.modules[m]
-
-    def find_module(self, name, path=None):
-        # type: (str, Sequence[Union[bytes, str]]) -> Any
-        # check if name is (or is a descendant of) one of our base_packages
-        for n in self.names:
-            if n == name or name.startswith(n + '.'):
-                return self
-        return None
-
-    def load_module(self, name):
-        # type: (str) -> ModuleType
-        if name in sys.modules:
-            # module has already been imported, return it
-            return sys.modules[name]
-        else:
-            logger.debug('[autodoc] adding a mock module %s!', name)
-            module = _MockModule(name, self)
-            sys.modules[name] = module
-            self.mocked_modules.append(name)
-            return module
-
-
 class MockLoader(Loader):
     """A loader for mocking."""
     def __init__(self, finder):
diff --git a/sphinx/ext/mathbase.py b/sphinx/ext/mathbase.py
deleted file mode 100644
index 0c89fd1ed..000000000
--- a/sphinx/ext/mathbase.py
+++ /dev/null
@@ -1,84 +0,0 @@
-"""
-    sphinx.ext.mathbase
-    ~~~~~~~~~~~~~~~~~~~
-
-    Set up math support in source files and LaTeX/text output.
-
-    :copyright: Copyright 2007-2019 by the Sphinx team, see AUTHORS.
-    :license: BSD, see LICENSE for details.
-"""
-
-import warnings
-
-from docutils import nodes
-from docutils.parsers.rst.roles import math_role as math_role_base
-
-from sphinx.addnodes import math, math_block as displaymath  # NOQA  # to keep compatibility
-from sphinx.builders.latex.nodes import math_reference as eqref  # NOQA  # to keep compatibility
-from sphinx.deprecation import RemovedInSphinx30Warning
-from sphinx.directives.patches import MathDirective as MathDirectiveBase
-from sphinx.domains.math import MathDomain  # NOQA  # to keep compatibility
-from sphinx.domains.math import MathReferenceRole as EqXRefRole  # NOQA  # to keep compatibility
-
-if False:
-    # For type annotation
-    from typing import Callable, Tuple  # NOQA
-    from sphinx.application import Sphinx  # NOQA
-    from sphinx.writers.html import HTMLTranslator  # NOQA
-
-
-class MathDirective(MathDirectiveBase):
-    def run(self):
-        warnings.warn('sphinx.ext.mathbase.MathDirective is moved to '
-                      'sphinx.directives.patches package.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return super().run()
-
-
-def math_role(role, rawtext, text, lineno, inliner, options={}, content=[]):
-    warnings.warn('sphinx.ext.mathbase.math_role() is deprecated. '
-                  'Please use docutils.parsers.rst.roles.math_role() instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return math_role_base(role, rawtext, text, lineno, inliner, options, content)
-
-
-def get_node_equation_number(writer, node):
-    # type: (HTMLTranslator, nodes.math_block) -> str
-    warnings.warn('sphinx.ext.mathbase.get_node_equation_number() is moved to '
-                  'sphinx.util.math package.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    from sphinx.util.math import get_node_equation_number
-    return get_node_equation_number(writer, node)
-
-
-def wrap_displaymath(text, label, numbering):
-    # type: (str, str, bool) -> str
-    warnings.warn('sphinx.ext.mathbase.wrap_displaymath() is moved to '
-                  'sphinx.util.math package.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    from sphinx.util.math import wrap_displaymath
-    return wrap_displaymath(text, label, numbering)
-
-
-def is_in_section_title(node):
-    # type: (nodes.Element) -> bool
-    """Determine whether the node is in a section title"""
-    from sphinx.util.nodes import traverse_parent
-
-    warnings.warn('is_in_section_title() is deprecated.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-
-    for ancestor in traverse_parent(node):
-        if isinstance(ancestor, nodes.title) and \
-           isinstance(ancestor.parent, nodes.section):
-            return True
-    return False
-
-
-def setup_math(app, htmlinlinevisitors, htmldisplayvisitors):
-    # type: (Sphinx, Tuple[Callable, Callable], Tuple[Callable, Callable]) -> None
-    warnings.warn('setup_math() is deprecated. '
-                  'Please use app.add_html_math_renderer() instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-
-    app.add_html_math_renderer('unknown', htmlinlinevisitors, htmldisplayvisitors)
diff --git a/sphinx/ext/viewcode.py b/sphinx/ext/viewcode.py
index 2997dc216..5de8f7f5e 100644
--- a/sphinx/ext/viewcode.py
+++ b/sphinx/ext/viewcode.py
@@ -9,13 +9,11 @@
 """
 
 import traceback
-import warnings
 
 from docutils import nodes
 
 import sphinx
 from sphinx import addnodes
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.locale import _, __
 from sphinx.pycode import ModuleAnalyzer
 from sphinx.util import get_full_modname, logging, status_iterator
@@ -238,14 +236,6 @@ def collect_pages(app):
     yield ('_modules/index', context, 'page.html')
 
 
-def migrate_viewcode_import(app, config):
-    # type: (Sphinx, Config) -> None
-    if config.viewcode_import is not None:
-        warnings.warn('viewcode_import was renamed to viewcode_follow_imported_members. '
-                      'Please update your configuration.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-
 def setup(app):
     # type: (Sphinx) -> Dict[str, Any]
     app.add_config_value('viewcode_import', None, False)
diff --git a/sphinx/highlighting.py b/sphinx/highlighting.py
index c53149ce6..c194738f8 100644
--- a/sphinx/highlighting.py
+++ b/sphinx/highlighting.py
@@ -8,9 +8,6 @@
     :license: BSD, see LICENSE for details.
 """
 
-import html
-import warnings
-
 from pygments import highlight
 from pygments.filters import ErrorToken
 from pygments.formatters import HtmlFormatter, LatexFormatter
@@ -21,8 +18,6 @@ from pygments.lexers import PythonLexer, Python3Lexer, PythonConsoleLexer, \
 from pygments.styles import get_style_by_name
 from pygments.util import ClassNotFound
 
-from sphinx.deprecation import RemovedInSphinx30Warning
-from sphinx.ext import doctest
 from sphinx.locale import __
 from sphinx.pygments_styles import SphinxStyle, NoneStyle
 from sphinx.util import logging
@@ -66,8 +61,8 @@ class PygmentsBridge:
     html_formatter = HtmlFormatter
     latex_formatter = LatexFormatter
 
-    def __init__(self, dest='html', stylename='sphinx', trim_doctest_flags=None):
-        # type: (str, str, bool) -> None
+    def __init__(self, dest='html', stylename='sphinx'):
+        # type: (str, str) -> None
         self.dest = dest
         if stylename is None or stylename == 'sphinx':
             style = SphinxStyle
@@ -86,30 +81,11 @@ class PygmentsBridge:
             self.formatter = self.latex_formatter
             self.formatter_args['commandprefix'] = 'PYG'
 
-        self.trim_doctest_flags = trim_doctest_flags
-        if trim_doctest_flags is not None:
-            warnings.warn('trim_doctest_flags option for PygmentsBridge is now deprecated.',
-                          RemovedInSphinx30Warning, stacklevel=2)
-
     def get_formatter(self, **kwargs):
         # type: (Any) -> Formatter
         kwargs.update(self.formatter_args)
         return self.formatter(**kwargs)
 
-    def unhighlighted(self, source):
-        # type: (str) -> str
-        warnings.warn('PygmentsBridge.unhighlighted() is now deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        if self.dest == 'html':
-            return '<pre>' + html.escape(source) + '</pre>\n'
-        else:
-            # first, escape highlighting characters like Pygments does
-            source = source.translate(escape_hl_chars)
-            # then, escape all characters nonrepresentable in LaTeX
-            source = source.translate(tex_hl_escape_map_new)
-            return '\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n' + \
-                   source + '\\end{Verbatim}\n'
-
     def highlight_block(self, source, lang, opts=None, location=None, force=False, **kwargs):
         # type: (str, str, Any, Any, bool, Any) -> str
         if not isinstance(source, str):
@@ -145,11 +121,6 @@ class PygmentsBridge:
                 else:
                     lexer.add_filter('raiseonerror')
 
-        # trim doctest options if wanted
-        if isinstance(lexer, PythonConsoleLexer) and self.trim_doctest_flags:
-            source = doctest.blankline_re.sub('', source)
-            source = doctest.doctestopt_re.sub('', source)
-
         # highlight via Pygments
         formatter = self.get_formatter(**kwargs)
         try:
diff --git a/sphinx/io.py b/sphinx/io.py
index b5b57d065..105ed4397 100644
--- a/sphinx/io.py
+++ b/sphinx/io.py
@@ -8,17 +8,14 @@
     :license: BSD, see LICENSE for details.
 """
 import codecs
-import warnings
 from typing import Any
 
 from docutils.core import Publisher
 from docutils.io import FileInput, NullOutput
 from docutils.parsers.rst import Parser as RSTParser
 from docutils.readers import standalone
-from docutils.statemachine import StringList, string2lines
 from docutils.writers import UnfilteredWriter
 
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.transforms import (
     AutoIndexUpgrader, DoctreeReadEvent, FigureAligner, SphinxTransformer
 )
@@ -29,7 +26,6 @@ from sphinx.transforms.references import SphinxDomains
 from sphinx.util import logging
 from sphinx.util import UnicodeDecodeErrorHandler
 from sphinx.util.docutils import LoggingReporter
-from sphinx.util.rst import append_epilog, docinfo_re, prepend_prolog
 from sphinx.versioning import UIDTransform
 
 if False:
@@ -136,19 +132,6 @@ class SphinxI18nReader(SphinxBaseReader):
 
         super().__init__(app, *args, **kwargs)
 
-    def set_lineno_for_reporter(self, lineno):
-        # type: (int) -> None
-        """Stores the source line number of original text."""
-        warnings.warn('SphinxI18nReader.set_lineno_for_reporter() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-    @property
-    def line(self):
-        # type: () -> int
-        warnings.warn('SphinxI18nReader.line is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return 0
-
 
 class SphinxDummyWriter(UnfilteredWriter):
     """Dummy writer module used for generating doctree."""
@@ -166,99 +149,14 @@ def SphinxDummySourceClass(source, *args, **kwargs):
     return source
 
 
-class SphinxBaseFileInput(FileInput):
-    """A base class of SphinxFileInput.
-
-    It supports to replace unknown Unicode characters to '?'.
-    """
-
-    def __init__(self, app, env, *args, **kwds):
-        # type: (Sphinx, BuildEnvironment, Any, Any) -> None
-        self.app = app
-        self.env = env
-
-        warnings.warn('%s is deprecated.' % self.__class__.__name__,
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-        kwds['error_handler'] = 'sphinx'  # py3: handle error on open.
-        super().__init__(*args, **kwds)
-
-    def warn_and_replace(self, error):
-        # type: (Any) -> Tuple
-        return UnicodeDecodeErrorHandler(self.env.docname)(error)
-
-
 class SphinxFileInput(FileInput):
     """A basic FileInput for Sphinx."""
-    supported = ('*',)  # RemovedInSphinx30Warning
-
     def __init__(self, *args, **kwargs):
         # type: (Any, Any) -> None
         kwargs['error_handler'] = 'sphinx'
         super().__init__(*args, **kwargs)
 
 
-class SphinxRSTFileInput(SphinxBaseFileInput):
-    """A reST FileInput for Sphinx.
-
-    This FileInput automatically prepends and appends text by :confval:`rst_prolog` and
-    :confval:`rst_epilog`.
-
-    .. important::
-
-       This FileInput uses an instance of ``StringList`` as a return value of ``read()``
-       method to indicate original source filename and line numbers after prepending and
-       appending.
-       For that reason, ``sphinx.parsers.RSTParser`` should be used with this to parse
-       a content correctly.
-    """
-    supported = ('restructuredtext',)
-
-    def prepend_prolog(self, text, prolog):
-        # type: (StringList, str) -> None
-        docinfo = self.count_docinfo_lines(text)
-        if docinfo:
-            # insert a blank line after docinfo
-            text.insert(docinfo, '', '<generated>', 0)
-            docinfo += 1
-
-        # insert prolog (after docinfo if exists)
-        for lineno, line in enumerate(prolog.splitlines()):
-            text.insert(docinfo + lineno, line, '<rst_prolog>', lineno)
-
-        text.insert(docinfo + lineno + 1, '', '<generated>', 0)
-
-    def append_epilog(self, text, epilog):
-        # type: (StringList, str) -> None
-        # append a blank line and rst_epilog
-        text.append('', '<generated>', 0)
-        for lineno, line in enumerate(epilog.splitlines()):
-            text.append(line, '<rst_epilog>', lineno)
-
-    def read(self):  # type: ignore
-        # type: () -> StringList
-        inputstring = super().read()
-        lines = string2lines(inputstring, convert_whitespace=True)
-        content = StringList()
-        for lineno, line in enumerate(lines):
-            content.append(line, self.source_path, lineno)
-
-        prepend_prolog(content, self.env.config.rst_prolog)
-        append_epilog(content, self.env.config.rst_epilog)
-
-        return content
-
-    def count_docinfo_lines(self, content):
-        # type: (StringList) -> int
-        if len(content) == 0:
-            return 0
-        else:
-            for lineno, line in enumerate(content.data):
-                if not docinfo_re.match(line):
-                    break
-            return lineno
-
-
 class FiletypeNotFoundError(Exception):
     pass
 
diff --git a/sphinx/locale/__init__.py b/sphinx/locale/__init__.py
index 6ae20d0d0..d18d075d4 100644
--- a/sphinx/locale/__init__.py
+++ b/sphinx/locale/__init__.py
@@ -10,12 +10,9 @@
 
 import gettext
 import locale
-import warnings
 from collections import UserString, defaultdict
 from gettext import NullTranslations
 
-from sphinx.deprecation import RemovedInSphinx30Warning
-
 if False:
     # For type annotation
     from typing import Any, Callable, Dict, Iterable, List, Tuple, Union  # NOQA
@@ -127,26 +124,6 @@ class _TranslationProxy(UserString):
             return '<%s broken>' % self.__class__.__name__
 
 
-def mygettext(string):
-    # type: (str) -> str
-    """Used instead of _ when creating TranslationProxies, because _ is
-    not bound yet at that time.
-    """
-    warnings.warn('sphinx.locale.mygettext() is deprecated.  Please use `_()` instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return _(string)
-
-
-def lazy_gettext(string):
-    # type: (str) -> str
-    """A lazy version of `gettext`."""
-    # if isinstance(string, _TranslationProxy):
-    #     return string
-    warnings.warn('sphinx.locale.laxy_gettext() is deprecated.  Please use `_()` instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return _TranslationProxy(mygettext, string)  # type: ignore
-
-
 translators = defaultdict(NullTranslations)  # type: Dict[Tuple[str, str], NullTranslations]
 
 
@@ -295,12 +272,6 @@ _ = get_translation('sphinx')
 __ = get_translation('sphinx', 'console')
 
 
-def l_(*args):
-    warnings.warn('sphinx.locale.l_() is deprecated.  Please use `_()` instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return _(*args)
-
-
 # labels
 admonitionlabels = {
     'attention': _('Attention'),
diff --git a/sphinx/make_mode.py b/sphinx/make_mode.py
deleted file mode 100644
index c1da2a5fa..000000000
--- a/sphinx/make_mode.py
+++ /dev/null
@@ -1,38 +0,0 @@
-"""
-    sphinx.make_mode
-    ~~~~~~~~~~~~~~~~
-
-    sphinx-build -M command-line handling.
-
-    This replaces the old, platform-dependent and once-generated content
-    of Makefile / make.bat.
-
-    This is in its own module so that importing it is fast.  It should not
-    import the main Sphinx modules (like sphinx.applications, sphinx.builders).
-
-    :copyright: Copyright 2007-2019 by the Sphinx team, see AUTHORS.
-    :license: BSD, see LICENSE for details.
-"""
-
-import warnings
-
-from sphinx.cmd import make_mode
-from sphinx.deprecation import RemovedInSphinx30Warning
-
-
-BUILDERS = make_mode.BUILDERS
-
-
-class Make(make_mode.Make):
-    def __init__(self, *args):
-        warnings.warn('sphinx.make_mode.Make is deprecated. '
-                      'Please use sphinx.cmd.make_mode.Make instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        super().__init__(*args)
-
-
-def run_make_mode(args):
-    warnings.warn('sphinx.make_mode.run_make_mode() is deprecated. '
-                  'Please use sphinx.cmd.make_mode.run_make_mode() instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    return make_mode.run_make_mode(args)
diff --git a/sphinx/registry.py b/sphinx/registry.py
index 311270ccb..32dbd2f55 100644
--- a/sphinx/registry.py
+++ b/sphinx/registry.py
@@ -9,14 +9,11 @@
 """
 
 import traceback
-import warnings
-from inspect import isclass
 from types import MethodType
 
 from docutils.parsers.rst import Directive
 from pkg_resources import iter_entry_points
 
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.domains import ObjType
 from sphinx.domains.std import GenericObject, Target
 from sphinx.errors import ExtensionError, SphinxError, VersionRequirementError
@@ -25,7 +22,6 @@ from sphinx.locale import __
 from sphinx.parsers import Parser as SphinxParser
 from sphinx.roles import XRefRole
 from sphinx.util import logging
-from sphinx.util.docutils import directive_helper
 from sphinx.util.logging import prefixed_warnings
 
 if False:
@@ -181,18 +177,9 @@ class SphinxComponentRegistry:
 
             yield domain
 
-    def override_domain(self, domain):
-        # type: (Type[Domain]) -> None
-        warnings.warn('registry.override_domain() is deprecated. '
-                      'Use app.add_domain(domain, override=True) instead.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        self.add_domain(domain, override=True)
-
-    def add_directive_to_domain(self, domain, name, obj, has_content=None, argument_spec=None,
-                                override=False, **option_spec):
-        # type: (str, str, Any, bool, Any, bool, Any) -> None
-        logger.debug('[app] adding directive to domain: %r',
-                     (domain, name, obj, has_content, argument_spec, option_spec))
+    def add_directive_to_domain(self, domain, name, cls, override=False):
+        # type: (str, str, Type[Directive], bool) -> None
+        logger.debug('[app] adding directive to domain: %r', (domain, name, cls))
         if domain not in self.domains:
             raise ExtensionError(__('domain %s not yet registered') % domain)
 
@@ -200,10 +187,7 @@ class SphinxComponentRegistry:
         if name in directives and not override:
             raise ExtensionError(__('The %r directive is already registered to domain %s') %
                                  (name, domain))
-        if not isclass(obj) or not issubclass(obj, Directive):
-            directives[name] = directive_helper(obj, has_content, argument_spec, **option_spec)
-        else:
-            directives[name] = obj
+        directives[name] = cls
 
     def add_role_to_domain(self, domain, name, role, override=False):
         # type: (str, str, Union[RoleFunction, XRefRole], bool) -> None
@@ -279,29 +263,9 @@ class SphinxComponentRegistry:
         else:
             self.source_suffix[suffix] = filetype
 
-    def add_source_parser(self, *args, **kwargs):
-        # type: (Any, bool) -> None
-        logger.debug('[app] adding search source_parser: %r', args)
-        if len(args) == 1:
-            # new sytle arguments: (source_parser)
-            suffix = None       # type: str
-            parser = args[0]    # type: Type[Parser]
-        else:
-            # old style arguments: (suffix, source_parser)
-            warnings.warn('app.add_source_parser() does not support suffix argument. '
-                          'Use app.add_source_suffix() instead.',
-                          RemovedInSphinx30Warning, stacklevel=3)
-            suffix = args[0]
-            parser = args[1]
-
-        if suffix:
-            self.add_source_suffix(suffix, suffix, override=True)
-
-        if len(parser.supported) == 0:
-            warnings.warn('Old source_parser has been detected. Please fill Parser.supported '
-                          'attribute: %s' % parser.__name__,
-                          RemovedInSphinx30Warning, stacklevel=3)
-
+    def add_source_parser(self, parser, **kwargs):
+        # type: (Type[Parser], bool) -> None
+        logger.debug('[app] adding search source_parser: %r', parser)
         # create a map from filetype to parser
         for filetype in parser.supported:
             if filetype in self.source_parsers and not kwargs.get('override'):
@@ -310,12 +274,6 @@ class SphinxComponentRegistry:
             else:
                 self.source_parsers[filetype] = parser
 
-        # also maps suffix to parser
-        #
-        # This rescues old styled parsers which does not have ``supported`` filetypes.
-        if suffix:
-            self.source_parsers[suffix] = parser
-
     def get_source_parser(self, filetype):
         # type: (str) -> Type[Parser]
         try:
@@ -335,16 +293,6 @@ class SphinxComponentRegistry:
             parser.set_application(app)
         return parser
 
-    def add_source_input(self, input_class, override=False):
-        # type: (Type[SphinxFileInput], bool) -> None
-        warnings.warn('registry.source_input() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        for filetype in input_class.supported:
-            if filetype in self.source_inputs and not override:
-                raise ExtensionError(__('source_input for %r is already registered') %
-                                     filetype)
-            self.source_inputs[filetype] = input_class
-
     def get_source_input(self, filetype):
         # type: (str) -> Type[Input]
         try:
diff --git a/sphinx/search/ja.py b/sphinx/search/ja.py
index 0c11af74d..e1f18209a 100644
--- a/sphinx/search/ja.py
+++ b/sphinx/search/ja.py
@@ -19,7 +19,6 @@
 import os
 import re
 import sys
-import warnings
 
 try:
     import MeCab
@@ -33,7 +32,6 @@ try:
 except ImportError:
     janome_module = False
 
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.errors import SphinxError, ExtensionError
 from sphinx.search import SearchLanguage
 from sphinx.util import import_object
@@ -543,22 +541,10 @@ class SearchJapanese(SearchLanguage):
     """
     lang = 'ja'
     language_name = 'Japanese'
-    splitters = {
-        'default': 'sphinx.search.ja.DefaultSplitter',
-        'mecab': 'sphinx.search.ja.MecabSplitter',
-        'janome': 'sphinx.search.ja.JanomeSplitter',
-    }
 
     def init(self, options):
         # type: (Dict) -> None
-        type = options.get('type', 'sphinx.search.ja.DefaultSplitter')
-        if type in self.splitters:
-            dotted_path = self.splitters[type]
-            warnings.warn('html_search_options["type"]: %s is deprecated. '
-                          'Please give "%s" instead.' % (type, dotted_path),
-                          RemovedInSphinx30Warning, stacklevel=2)
-        else:
-            dotted_path = type
+        dotted_path = options.get('type', 'sphinx.search.ja.DefaultSplitter')
         try:
             self.splitter = import_object(dotted_path)(options)
         except ExtensionError:
diff --git a/sphinx/transforms/post_transforms/compat.py b/sphinx/transforms/post_transforms/compat.py
deleted file mode 100644
index 67b67f8d4..000000000
--- a/sphinx/transforms/post_transforms/compat.py
+++ /dev/null
@@ -1,90 +0,0 @@
-"""
-    sphinx.transforms.post_transforms.compat
-    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-    Post transforms for compatibility
-
-    :copyright: Copyright 2007-2019 by the Sphinx team, see AUTHORS.
-    :license: BSD, see LICENSE for details.
-"""
-
-import warnings
-
-from docutils import nodes
-from docutils.writers.docutils_xml import XMLTranslator
-
-from sphinx.addnodes import math_block, displaymath
-from sphinx.deprecation import RemovedInSphinx30Warning
-from sphinx.transforms import SphinxTransform
-from sphinx.util import logging
-
-if False:
-    # For type annotation
-    from typing import Any, Dict  # NOQA
-    from sphinx.application import Sphinx  # NOQA
-
-logger = logging.getLogger(__name__)
-
-
-class MathNodeMigrator(SphinxTransform):
-    """Migrate a math node to docutils'.
-
-    For a long time, Sphinx uses an original node for math. Since 1.8,
-    Sphinx starts to use a math node of docutils'.  This transform converts
-    old and new nodes to keep compatibility.
-    """
-    default_priority = 999
-
-    def apply(self, **kwargs):
-        # type: (Any) -> None
-        for math_node in self.document.traverse(nodes.math):
-            # case: old styled ``math`` node generated by old extensions
-            if len(math_node) == 0:
-                warnings.warn("math node for Sphinx was replaced by docutils'. "
-                              "Please use ``docutils.nodes.math`` instead.",
-                              RemovedInSphinx30Warning)
-                equation = math_node['latex']
-                math_node += nodes.Text(equation, equation)
-
-        translator = self.app.builder.get_translator_class()
-        if hasattr(translator, 'visit_displaymath') and translator != XMLTranslator:
-            # case: old translators which does not support ``math_block`` node
-            warnings.warn("Translator for %s does not support math_block node'. "
-                          "Please update your extension." % translator,
-                          RemovedInSphinx30Warning)
-            for old_math_block_node in self.document.traverse(math_block):
-                alt = displaymath(latex=old_math_block_node.astext(),
-                                  number=old_math_block_node.get('number'),
-                                  label=old_math_block_node.get('label'),
-                                  nowrap=old_math_block_node.get('nowrap'),
-                                  docname=old_math_block_node.get('docname'))
-                old_math_block_node.replace_self(alt)
-        elif getattr(self.app.builder, 'math_renderer_name', None) == 'unknown':
-            # case: math extension provides old styled math renderer
-            for math_block_node in self.document.traverse(nodes.math_block):
-                math_block_node['latex'] = math_block_node.astext()
-
-        # case: old styled ``displaymath`` node generated by old extensions
-        for math_block_node in self.document.traverse(math_block):
-            if len(math_block_node) == 0:
-                warnings.warn("math node for Sphinx was replaced by docutils'. "
-                              "Please use ``docutils.nodes.math_block`` instead.",
-                              RemovedInSphinx30Warning)
-                if isinstance(math_block_node, displaymath):
-                    newnode = nodes.math_block('', math_block_node['latex'],
-                                               **math_block_node.attributes)
-                    math_block_node.replace_self(newnode)
-                else:
-                    latex = math_block_node['latex']
-                    math_block_node += nodes.Text(latex, latex)
-
-
-def setup(app):
-    # type: (Sphinx) -> Dict[str, Any]
-    app.add_post_transform(MathNodeMigrator)
-
-    return {
-        'version': 'builtin',
-        'parallel_read_safe': True,
-        'parallel_write_safe': True,
-    }
diff --git a/sphinx/util/__init__.py b/sphinx/util/__init__.py
index 2ebae8768..cc2cd9aa1 100644
--- a/sphinx/util/__init__.py
+++ b/sphinx/util/__init__.py
@@ -26,21 +26,18 @@ from os import path
 from time import mktime, strptime
 from urllib.parse import urlsplit, urlunsplit, quote_plus, parse_qsl, urlencode
 
-from docutils.utils import relative_path
-
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.errors import PycodeError, SphinxParallelError, ExtensionError
 from sphinx.locale import __
 from sphinx.util import logging
 from sphinx.util.console import strip_colors, colorize, bold, term_width_line  # type: ignore
-from sphinx.util.fileutil import copy_asset_file
 from sphinx.util import smartypants  # noqa
 
 # import other utilities; partly for backwards compatibility, so don't
 # prune unused ones indiscriminately
 from sphinx.util.osutil import (  # noqa
     SEP, os_path, relative_uri, ensuredir, walk, mtimes_of_files, movefile,
-    copyfile, copytimes, make_filename, ustrftime)
+    copyfile, copytimes, make_filename)
 from sphinx.util.nodes import (   # noqa
     nested_parse_with_titles, split_explicit_title, explicit_title_re,
     caption_ref_re)
@@ -196,36 +193,6 @@ class DownloadFiles(dict):
                 self.add_file(docname, filename)
 
 
-def copy_static_entry(source, targetdir, builder, context={},
-                      exclude_matchers=(), level=0):
-    # type: (str, str, Any, Dict, Tuple[Callable, ...], int) -> None
-    """[DEPRECATED] Copy a HTML builder static_path entry from source to targetdir.
-
-    Handles all possible cases of files, directories and subdirectories.
-    """
-    warnings.warn('sphinx.util.copy_static_entry is deprecated for removal',
-                  RemovedInSphinx30Warning, stacklevel=2)
-
-    if exclude_matchers:
-        relpath = relative_path(path.join(builder.srcdir, 'dummy'), source)
-        for matcher in exclude_matchers:
-            if matcher(relpath):
-                return
-    if path.isfile(source):
-        copy_asset_file(source, targetdir, context, builder.templates)
-    elif path.isdir(source):
-        ensuredir(targetdir)
-        for entry in os.listdir(source):
-            if entry.startswith('.'):
-                continue
-            newtarget = targetdir
-            if path.isdir(path.join(source, entry)):
-                newtarget = path.join(targetdir, entry)
-            copy_static_entry(path.join(source, entry), newtarget,
-                              builder, context, level=level + 1,
-                              exclude_matchers=exclude_matchers)
-
-
 _DEBUG_HEADER = '''\
 # Sphinx version: %s
 # Python version: %s (%s)
diff --git a/sphinx/util/compat.py b/sphinx/util/compat.py
index 5d8cbb3db..805c17e5d 100644
--- a/sphinx/util/compat.py
+++ b/sphinx/util/compat.py
@@ -14,9 +14,8 @@ import warnings
 from docutils.utils import get_source_line
 
 from sphinx import addnodes
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.transforms import SphinxTransform
-from sphinx.util import import_object
 
 if False:
     # For type annotation
@@ -25,18 +24,6 @@ if False:
     from sphinx.config import Config  # NOQA
 
 
-def deprecate_source_parsers(app, config):
-    # type: (Sphinx, Config) -> None
-    if config.source_parsers:
-        warnings.warn('The config variable "source_parsers" is deprecated. '
-                      'Please use app.add_source_parser() API instead.',
-                      RemovedInSphinx30Warning)
-        for suffix, parser in config.source_parsers.items():
-            if isinstance(parser, str):
-                parser = import_object(parser, 'source parser')
-            app.add_source_parser(suffix, parser)
-
-
 def register_application_for_autosummary(app):
     # type: (Sphinx) -> None
     """Register application object to autosummary module.
@@ -69,7 +56,6 @@ class IndexEntriesMigrator(SphinxTransform):
 def setup(app):
     # type: (Sphinx) -> Dict[str, Any]
     app.add_transform(IndexEntriesMigrator)
-    app.connect('config-inited', deprecate_source_parsers)
     app.connect('builder-inited', register_application_for_autosummary)
 
     return {
diff --git a/sphinx/util/docutils.py b/sphinx/util/docutils.py
index eebfec464..d38c780f4 100644
--- a/sphinx/util/docutils.py
+++ b/sphinx/util/docutils.py
@@ -10,8 +10,6 @@
 
 import os
 import re
-import types
-import warnings
 from contextlib import contextmanager
 from copy import copy
 from distutils.version import LooseVersion
@@ -21,13 +19,11 @@ from typing import IO, cast
 import docutils
 from docutils import nodes
 from docutils.io import FileOutput
-from docutils.parsers.rst import Directive, directives, roles, convert_directive_function
+from docutils.parsers.rst import Directive, directives, roles
 from docutils.statemachine import StateMachine
 from docutils.utils import Reporter, unescape
 
-from sphinx.deprecation import RemovedInSphinx30Warning
-from sphinx.errors import ExtensionError, SphinxError
-from sphinx.locale import __
+from sphinx.errors import SphinxError
 from sphinx.util import logging
 
 logger = logging.getLogger(__name__)
@@ -304,24 +300,6 @@ def is_html5_writer_available():
     return __version_info__ > (0, 13, 0)
 
 
-def directive_helper(obj, has_content=None, argument_spec=None, **option_spec):
-    # type: (Any, bool, Tuple[int, int, bool], Any) -> Any
-    warnings.warn('function based directive support is now deprecated. '
-                  'Use class based directive instead.',
-                  RemovedInSphinx30Warning)
-
-    if isinstance(obj, (types.FunctionType, types.MethodType)):
-        obj.content = has_content                       # type: ignore
-        obj.arguments = argument_spec or (0, 0, False)  # type: ignore
-        obj.options = option_spec                       # type: ignore
-        return convert_directive_function(obj)
-    else:
-        if has_content or argument_spec or option_spec:
-            raise ExtensionError(__('when adding directive classes, no '
-                                    'additional arguments may be given'))
-        return obj
-
-
 @contextmanager
 def switch_source_input(state, content):
     # type: (State, StringList) -> Generator[None, None, None]
diff --git a/sphinx/util/i18n.py b/sphinx/util/i18n.py
index e342b1246..89534f5ae 100644
--- a/sphinx/util/i18n.py
+++ b/sphinx/util/i18n.py
@@ -19,7 +19,7 @@ import babel.dates
 from babel.messages.mofile import write_mo
 from babel.messages.pofile import read_po
 
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.errors import SphinxError
 from sphinx.locale import __
 from sphinx.util import logging
@@ -161,10 +161,9 @@ def find_catalog_files(docname, srcdir, locale_dirs, lang, compaction):
     return files
 
 
-def find_catalog_source_files(locale_dirs, locale, domains=None, gettext_compact=None,
-                              charset='utf-8', force_all=False,
-                              excluded=Matcher([])):
-    # type: (List[str], str, List[str], bool, str, bool, Matcher) -> Set[CatalogInfo]
+def find_catalog_source_files(locale_dirs, locale, domains=None, charset='utf-8',
+                              force_all=False, excluded=Matcher([])):
+    # type: (List[str], str, List[str], str, bool, Matcher) -> Set[CatalogInfo]
     """
     :param list locale_dirs:
        list of path as `['locale_dir1', 'locale_dir2', ...]` to find
@@ -180,9 +179,6 @@ def find_catalog_source_files(locale_dirs, locale, domains=None, gettext_compact
     """
     warnings.warn('find_catalog_source_files() is deprecated.',
                   RemovedInSphinx40Warning, stacklevel=2)
-    if gettext_compact is not None:
-        warnings.warn('gettext_compact argument for find_catalog_source_files() '
-                      'is deprecated.', RemovedInSphinx30Warning, stacklevel=2)
 
     catalogs = set()  # type: Set[CatalogInfo]
 
diff --git a/sphinx/util/images.py b/sphinx/util/images.py
index 0e5f3e81b..76bffd88c 100644
--- a/sphinx/util/images.py
+++ b/sphinx/util/images.py
@@ -10,16 +10,12 @@
 
 import base64
 import imghdr
-import warnings
 from collections import OrderedDict
-from io import BytesIO
 from os import path
 from typing import NamedTuple
 
 import imagesize
 
-from sphinx.deprecation import RemovedInSphinx30Warning
-
 try:
     from PIL import Image
 except ImportError:
@@ -72,17 +68,11 @@ def guess_mimetype_for_stream(stream, default=None):
         return default
 
 
-def guess_mimetype(filename='', content=None, default=None):
-    # type: (str, bytes, str) -> str
+def guess_mimetype(filename, default=None):
+    # type: (str, str) -> str
     _, ext = path.splitext(filename.lower())
     if ext in mime_suffixes:
         return mime_suffixes[ext]
-    elif content:
-        # TODO: When the content argument is removed, make filename a required
-        # argument.
-        warnings.warn('The content argument of guess_mimetype() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return guess_mimetype_for_stream(BytesIO(content), default=default)
     elif path.exists(filename):
         with open(filename, 'rb') as f:
             return guess_mimetype_for_stream(f, default=default)
diff --git a/sphinx/util/inspect.py b/sphinx/util/inspect.py
index 89dd842e3..ff399c439 100644
--- a/sphinx/util/inspect.py
+++ b/sphinx/util/inspect.py
@@ -14,11 +14,9 @@ import inspect
 import re
 import sys
 import typing
-import warnings
 from functools import partial
 from io import StringIO
 
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.util import logging
 from sphinx.util.typing import NoneType
 
@@ -264,26 +262,6 @@ def is_builtin_class_method(obj, attr_name):
     return getattr(builtins, safe_getattr(cls, '__name__', '')) is cls  # type: ignore
 
 
-class Parameter:
-    """Fake parameter class for python2."""
-    POSITIONAL_ONLY = 0
-    POSITIONAL_OR_KEYWORD = 1
-    VAR_POSITIONAL = 2
-    KEYWORD_ONLY = 3
-    VAR_KEYWORD = 4
-    empty = object()
-
-    def __init__(self, name, kind=POSITIONAL_OR_KEYWORD, default=empty):
-        # type: (str, int, Any) -> None
-        self.name = name
-        self.kind = kind
-        self.default = default
-        self.annotation = self.empty
-
-        warnings.warn('sphinx.util.inspect.Parameter is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-
 class Signature:
     """The Signature object represents the call signature of a callable object and
     its return annotation.
diff --git a/sphinx/util/osutil.py b/sphinx/util/osutil.py
index 6a070a27a..4cd646f96 100644
--- a/sphinx/util/osutil.py
+++ b/sphinx/util/osutil.py
@@ -15,12 +15,11 @@ import os
 import re
 import shutil
 import sys
-import time
 import warnings
 from io import StringIO
 from os import path
 
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 
 if False:
     # For type annotation
@@ -148,28 +147,6 @@ def make_filename_from_project(project):
     return make_filename(project_suffix_re.sub('', project)).lower()
 
 
-def ustrftime(format, *args):
-    # type: (str, Any) -> str
-    """[DEPRECATED] strftime for unicode strings."""
-    warnings.warn('sphinx.util.osutil.ustrtime is deprecated for removal',
-                  RemovedInSphinx30Warning, stacklevel=2)
-
-    if not args:
-        # If time is not specified, try to use $SOURCE_DATE_EPOCH variable
-        # See https://wiki.debian.org/ReproducibleBuilds/TimestampsProposal
-        source_date_epoch = os.getenv('SOURCE_DATE_EPOCH')
-        if source_date_epoch is not None:
-            time_struct = time.gmtime(float(source_date_epoch))
-            args = [time_struct]  # type: ignore
-    # On Windows, time.strftime() and Unicode characters will raise UnicodeEncodeError.
-    # https://bugs.python.org/issue8304
-    try:
-        return time.strftime(format, *args)
-    except UnicodeEncodeError:
-        r = time.strftime(format.encode('unicode-escape').decode(), *args)
-        return r.encode().decode('unicode-escape')
-
-
 def relpath(path, start=os.curdir):
     # type: (str, str) -> str
     """Return a relative filepath to *path* either from the current directory or
diff --git a/sphinx/versioning.py b/sphinx/versioning.py
index c98d166bc..56c126da2 100644
--- a/sphinx/versioning.py
+++ b/sphinx/versioning.py
@@ -9,13 +9,11 @@
     :license: BSD, see LICENSE for details.
 """
 import pickle
-import warnings
 from itertools import product, zip_longest
 from operator import itemgetter
 from os import path
 from uuid import uuid4
 
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.transforms import SphinxTransform
 
 if False:
@@ -180,15 +178,6 @@ class UIDTransform(SphinxTransform):
             list(merge_doctrees(old_doctree, self.document, env.versioning_condition))
 
 
-def prepare(document):
-    # type: (nodes.document) -> None
-    """Simple wrapper for UIDTransform."""
-    warnings.warn('versioning.prepare() is deprecated. Use UIDTransform instead.',
-                  RemovedInSphinx30Warning, stacklevel=2)
-    transform = UIDTransform(document)
-    transform.apply()
-
-
 def setup(app):
     # type: (Sphinx) -> Dict[str, Any]
     app.add_transform(UIDTransform)
diff --git a/sphinx/writers/html.py b/sphinx/writers/html.py
index 3eb9a0911..60cc7d999 100644
--- a/sphinx/writers/html.py
+++ b/sphinx/writers/html.py
@@ -11,7 +11,6 @@
 import copy
 import os
 import posixpath
-import sys
 import warnings
 from typing import Iterable, cast
 
@@ -20,7 +19,7 @@ from docutils.writers.html4css1 import Writer, HTMLTranslator as BaseTranslator
 
 from sphinx import addnodes
 from sphinx.builders import Builder
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.locale import admonitionlabels, _, __
 from sphinx.util import logging
 from sphinx.util.docutils import SphinxTranslator
@@ -945,33 +944,3 @@ class HTMLTranslator(SphinxTranslator, BaseTranslator):
     def unknown_visit(self, node):
         # type: (nodes.Node) -> None
         raise NotImplementedError('Unknown node: ' + node.__class__.__name__)
-
-    # --------- METHODS FOR COMPATIBILITY --------------------------------------
-
-    @property
-    def highlightlang(self):
-        # type: () -> str
-        warnings.warn('HTMLTranslator.highlightlang is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.builder.config.highlight_language
-
-    @property
-    def highlightlang_base(self):
-        # type: () -> str
-        warnings.warn('HTMLTranslator.highlightlang_base is deprecated.',
-                      RemovedInSphinx30Warning)
-        return self.builder.config.highlight_language
-
-    @property
-    def highlightopts(self):
-        # type: () -> str
-        warnings.warn('HTMLTranslator.highlightopts is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.builder.config.highlight_options
-
-    @property
-    def highlightlinenothreshold(self):
-        # type: () -> int
-        warnings.warn('HTMLTranslator.highlightlinenothreshold is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return sys.maxsize
diff --git a/sphinx/writers/html5.py b/sphinx/writers/html5.py
index 646d6cc31..afab35950 100644
--- a/sphinx/writers/html5.py
+++ b/sphinx/writers/html5.py
@@ -10,7 +10,6 @@
 
 import os
 import posixpath
-import sys
 import warnings
 from typing import Iterable, cast
 
@@ -19,7 +18,7 @@ from docutils.writers.html5_polyglot import HTMLTranslator as BaseTranslator
 
 from sphinx import addnodes
 from sphinx.builders import Builder
-from sphinx.deprecation import RemovedInSphinx30Warning, RemovedInSphinx40Warning
+from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.locale import admonitionlabels, _, __
 from sphinx.util import logging
 from sphinx.util.docutils import SphinxTranslator
@@ -882,33 +881,3 @@ class HTML5Translator(SphinxTranslator, BaseTranslator):
     def unknown_visit(self, node):
         # type: (nodes.Node) -> None
         raise NotImplementedError('Unknown node: ' + node.__class__.__name__)
-
-    # --------- METHODS FOR COMPATIBILITY --------------------------------------
-
-    @property
-    def highlightlang(self):
-        # type: () -> str
-        warnings.warn('HTMLTranslator.highlightlang is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.builder.config.highlight_language
-
-    @property
-    def highlightlang_base(self):
-        # type: () -> str
-        warnings.warn('HTMLTranslator.highlightlang_base is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.builder.config.highlight_language
-
-    @property
-    def highlightopts(self):
-        # type: () -> str
-        warnings.warn('HTMLTranslator.highlightopts is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return self.builder.config.highlight_options
-
-    @property
-    def highlightlinenothreshold(self):
-        # type: () -> int
-        warnings.warn('HTMLTranslator.highlightlinenothreshold is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return sys.maxsize
diff --git a/sphinx/writers/latex.py b/sphinx/writers/latex.py
index c5be44b18..b45a95eef 100644
--- a/sphinx/writers/latex.py
+++ b/sphinx/writers/latex.py
@@ -12,7 +12,6 @@
 """
 
 import re
-import sys
 import warnings
 from collections import defaultdict
 from os import path
@@ -22,9 +21,7 @@ from docutils import nodes, writers
 
 from sphinx import addnodes
 from sphinx import highlighting
-from sphinx.deprecation import (
-    RemovedInSphinx30Warning, RemovedInSphinx40Warning, deprecated_alias
-)
+from sphinx.deprecation import RemovedInSphinx40Warning, deprecated_alias
 from sphinx.domains.std import StandardDomain
 from sphinx.errors import SphinxError
 from sphinx.locale import admonitionlabels, _, __
@@ -284,20 +281,6 @@ class Table:
                                                 # (cell = rectangular area)
         self.cell_id = 0                        # last assigned cell_id
 
-    @property
-    def caption_footnotetexts(self):
-        # type: () -> List[str]
-        warnings.warn('table.caption_footnotetexts is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return []
-
-    @property
-    def header_footnotetexts(self):
-        # type: () -> List[str]
-        warnings.warn('table.header_footnotetexts is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return []
-
     def is_longtable(self):
         # type: () -> bool
         """True if and only if table uses longtable environment."""
@@ -653,27 +636,6 @@ class LaTeXTranslator(SphinxTranslator):
         self.body = self.bodystack.pop()
         return body
 
-    def restrict_footnote(self, node):
-        # type: (nodes.Element) -> None
-        warnings.warn('LaTeXWriter.restrict_footnote() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-        if self.footnote_restricted is None:
-            self.footnote_restricted = node
-            self.pending_footnotes = []
-
-    def unrestrict_footnote(self, node):
-        # type: (nodes.Element) -> None
-        warnings.warn('LaTeXWriter.unrestrict_footnote() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-        if self.footnote_restricted == node:
-            self.footnote_restricted = None
-            for footnode in self.pending_footnotes:
-                footnode['footnotetext'] = True
-                footnode.walkabout(self)
-            self.pending_footnotes = []
-
     def format_docclass(self, docclass):
         # type: (str) -> str
         """ prepends prefix to sphinx document classes
@@ -1781,8 +1743,8 @@ class LaTeXTranslator(SphinxTranslator):
         # type: (nodes.Element) -> None
         self.body.append('\n\\end{flushright}\n')
 
-    def visit_index(self, node, scre = None):
-        # type: (nodes.Element, Pattern) -> None
+    def visit_index(self, node):
+        # type: (nodes.Element) -> None
         def escape(value):
             value = self.encode(value)
             value = value.replace(r'\{', r'\sphinxleftcurlybrace{}')
@@ -1799,10 +1761,6 @@ class LaTeXTranslator(SphinxTranslator):
             else:
                 return '\\spxentry{%s}' % string
 
-        if scre:
-            warnings.warn(('LaTeXTranslator.visit_index() optional argument '
-                           '"scre" is deprecated. It is ignored.'),
-                          RemovedInSphinx30Warning, stacklevel=2)
         if not node.get('inline', True):
             self.body.append('\n')
         entries = node['entries']
@@ -2496,70 +2454,6 @@ class LaTeXTranslator(SphinxTranslator):
             fnotes[num] = [newnode, False]
         return fnotes
 
-    @property
-    def footnotestack(self):
-        # type: () -> List[Dict[str, List[Union[collected_footnote, bool]]]]
-        warnings.warn('LaTeXWriter.footnotestack is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return []
-
-    @property
-    def bibitems(self):
-        # type: () -> List[List[str]]
-        warnings.warn('LaTeXTranslator.bibitems() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return []
-
-    @property
-    def in_container_literal_block(self):
-        # type: () -> int
-        warnings.warn('LaTeXTranslator.in_container_literal_block is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return 0
-
-    @property
-    def next_section_ids(self):
-        # type: () -> Set[str]
-        warnings.warn('LaTeXTranslator.next_section_ids is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return set()
-
-    @property
-    def next_hyperlink_ids(self):
-        # type: () -> Dict
-        warnings.warn('LaTeXTranslator.next_hyperlink_ids is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return {}
-
-    def push_hyperlink_ids(self, figtype, ids):
-        # type: (str, Set[str]) -> None
-        warnings.warn('LaTeXTranslator.push_hyperlink_ids() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        pass
-
-    def pop_hyperlink_ids(self, figtype):
-        # type: (str) -> Set[str]
-        warnings.warn('LaTeXTranslator.pop_hyperlink_ids() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return set()
-
-    @property
-    def hlsettingstack(self):
-        # type: () -> List[List[Union[str, int]]]
-        warnings.warn('LaTeXTranslator.hlsettingstack is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-        return [[self.builder.config.highlight_language, sys.maxsize]]
-
-    def check_latex_elements(self):
-        # type: () -> None
-        warnings.warn('check_latex_elements() is deprecated.',
-                      RemovedInSphinx30Warning, stacklevel=2)
-
-        for key in self.builder.config.latex_elements:
-            if key not in self.elements:
-                msg = __("Unknown configure key: latex_elements[%r] is ignored.")
-                logger.warning(msg % key)
-
     def babel_defmacro(self, name, definition):
         # type: (str, str) -> str
         warnings.warn('babel_defmacro() is deprecated.',
@@ -2574,17 +2468,6 @@ class LaTeXTranslator(SphinxTranslator):
 
         return ('%s\\def%s{%s}%s\n' % (prefix, name, definition, suffix))
 
-    def _make_visit_admonition(name):  # type: ignore
-        # type: (str) -> Callable[[LaTeXTranslator, nodes.Element], None]
-        warnings.warn('LaTeXTranslator._make_visit_admonition() is deprecated.',
-                      RemovedInSphinx30Warning)
-
-        def visit_admonition(self, node):
-            # type: (nodes.Element) -> None
-            self.body.append('\n\\begin{sphinxadmonition}{%s}{%s:}' %
-                             (name, admonitionlabels[name]))
-        return visit_admonition
-
     def generate_numfig_format(self, builder):
         # type: (LaTeXBuilder) -> str
         warnings.warn('generate_numfig_format() is deprecated.',
@@ -2627,16 +2510,9 @@ class LaTeXTranslator(SphinxTranslator):
 
 
 # Import old modules here for compatibility
-from sphinx.builders.latex.transforms import URI_SCHEMES, ShowUrlsTransform  # NOQA
 from sphinx.builders.latex.util import ExtBabel  # NOQA
 
 
-deprecated_alias('sphinx.writers.latex',
-                 {
-                     'ShowUrlsTransform': ShowUrlsTransform,
-                     'URI_SCHEMES': URI_SCHEMES,
-                 },
-                 RemovedInSphinx30Warning)
 deprecated_alias('sphinx.writers.latex',
                  {
                      'ExtBabel': ExtBabel,
diff --git a/sphinx/writers/texinfo.py b/sphinx/writers/texinfo.py
index 4262ccd66..77d3dcb69 100644
--- a/sphinx/writers/texinfo.py
+++ b/sphinx/writers/texinfo.py
@@ -10,14 +10,12 @@
 
 import re
 import textwrap
-import warnings
 from os import path
 from typing import Iterable, cast
 
 from docutils import nodes, writers
 
 from sphinx import addnodes, __display_version__
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.errors import ExtensionError
 from sphinx.locale import admonitionlabels, _, __
 from sphinx.util import logging
@@ -1745,13 +1743,3 @@ class TexinfoTranslator(SphinxTranslator):
         self.body.append('\n\n@example\n%s\n@end example\n\n' %
                          self.escape_arg(node.astext()))
         raise nodes.SkipNode
-
-    def _make_visit_admonition(name):  # type: ignore
-        # type: (str) -> Callable[[TexinfoTranslator, nodes.Element], None]
-        warnings.warn('TexinfoTranslator._make_visit_admonition() is deprecated.',
-                      RemovedInSphinx30Warning)
-
-        def visit(self, node):
-            # type: (nodes.Element) -> None
-            self.visit_admonition(node, admonitionlabels[name])
-        return visit
diff --git a/sphinx/writers/text.py b/sphinx/writers/text.py
index 1447510c3..47ab9f2e4 100644
--- a/sphinx/writers/text.py
+++ b/sphinx/writers/text.py
@@ -11,7 +11,6 @@ import math
 import os
 import re
 import textwrap
-import warnings
 from itertools import groupby, chain
 from typing import Iterable, cast
 
@@ -19,7 +18,6 @@ from docutils import nodes, writers
 from docutils.utils import column_width
 
 from sphinx import addnodes
-from sphinx.deprecation import RemovedInSphinx30Warning
 from sphinx.locale import admonitionlabels, _
 from sphinx.util.docutils import SphinxTranslator
 
@@ -1368,13 +1366,3 @@ class TextTranslator(SphinxTranslator):
     def unknown_visit(self, node):
         # type: (nodes.Node) -> None
         raise NotImplementedError('Unknown node: ' + node.__class__.__name__)
-
-    def _make_depart_admonition(name):  # type: ignore
-        # type: (str) -> Callable[[TextTranslator, nodes.Element], None]
-        warnings.warn('TextTranslator._make_depart_admonition() is deprecated.',
-                      RemovedInSphinx30Warning)
-
-        def depart_admonition(self, node):
-            # type: (nodes.Element) -> None
-            self.end_state(first=admonitionlabels[name] + ': ')
-        return depart_admonition
diff --git a/tests/roots/test-add_source_parser/conf.py b/tests/roots/test-add_source_parser/conf.py
index 9ff50b21e..2acd4d24c 100644
--- a/tests/roots/test-add_source_parser/conf.py
+++ b/tests/roots/test-add_source_parser/conf.py
@@ -1,17 +1,8 @@
 import os
 import sys
 
-from docutils.parsers import Parser
-
 sys.path.insert(0, os.path.abspath('.'))
 
 
-class DummyMarkdownParser(Parser):
-    supported = ('markdown',)
-
-
 extensions = ['source_parser']
-source_suffix = ['.rst', '.md']
-source_parsers = {
-    '.md': DummyMarkdownParser
-}
+source_suffix = ['.rst']
diff --git a/tests/roots/test-ext-math-compat/conf.py b/tests/roots/test-ext-math-compat/conf.py
index 30d26f97c..85e3950a5 100644
--- a/tests/roots/test-ext-math-compat/conf.py
+++ b/tests/roots/test-ext-math-compat/conf.py
@@ -1,17 +1,18 @@
+from docutils import nodes
 from docutils.parsers.rst import Directive
 
-from sphinx.ext.mathbase import math, displaymath
-
 extensions = ['sphinx.ext.mathjax']
 
 
 def my_math_role(role, rawtext, text, lineno, inliner, options={}, content=[]):
-    return [math(latex='E = mc^2')], []
+    text = 'E = mc^2'
+    return [nodes.math(text, text)], []
 
 
 class MyMathDirective(Directive):
     def run(self):
-        return [displaymath(latex='E = mc^2')]
+        text = 'E = mc^2'
+        return [nodes.math_block(text, text)]
 
 
 def setup(app):
diff --git a/tests/test_application.py b/tests/test_application.py
index f10592b51..8c48e7500 100644
--- a/tests/test_application.py
+++ b/tests/test_application.py
@@ -61,20 +61,13 @@ def test_extension_in_blacklist(app, status, warning):
 
 
 @pytest.mark.sphinx(testroot='add_source_parser')
-@pytest.mark.filterwarnings('ignore:The config variable "source_parsers"')
-@pytest.mark.filterwarnings('ignore:app.add_source_parser\\(\\) does not support suffix')
 def test_add_source_parser(app, status, warning):
-    assert set(app.config.source_suffix) == {'.rst', '.md', '.test'}
+    assert set(app.config.source_suffix) == {'.rst', '.test'}
 
     # .rst; only in :confval:`source_suffix`
     assert '.rst' not in app.registry.get_source_parsers()
     assert app.registry.source_suffix['.rst'] is None
 
-    # .md; configured by :confval:`source_suffix` and :confval:`source_parsers`
-    assert '.md' in app.registry.get_source_parsers()
-    assert app.registry.source_suffix['.md'] == '.md'
-    assert app.registry.get_source_parsers()['.md'].__name__ == 'DummyMarkdownParser'
-
     # .test; configured by API
     assert app.registry.source_suffix['.test'] == 'test'
     assert 'test' in app.registry.get_source_parsers()
diff --git a/tests/test_autodoc.py b/tests/test_autodoc.py
index 27412a9da..cfb62d1ba 100644
--- a/tests/test_autodoc.py
+++ b/tests/test_autodoc.py
@@ -16,10 +16,7 @@ from warnings import catch_warnings
 import pytest
 from docutils.statemachine import ViewList
 
-from sphinx.ext.autodoc import (
-    ModuleLevelDocumenter, cut_lines, between, ALL,
-    merge_autodoc_default_flags, Options
-)
+from sphinx.ext.autodoc import ModuleLevelDocumenter, cut_lines, between, ALL, Options
 from sphinx.ext.autodoc.directive import DocumenterBridge, process_documenter_options
 from sphinx.testing.util import SphinxTestApp, Struct  # NOQA
 from sphinx.util import logging
@@ -1522,27 +1519,6 @@ def test_partialmethod(app):
     assert list(actual) == expected
 
 
-@pytest.mark.sphinx('html', testroot='ext-autodoc')
-@pytest.mark.filterwarnings('ignore:autodoc_default_flags is now deprecated.')
-def test_merge_autodoc_default_flags1(app):
-    app.config.autodoc_default_flags = ['members', 'undoc-members']
-    merge_autodoc_default_flags(app, app.config)
-    assert app.config.autodoc_default_options == {'members': None,
-                                                  'undoc-members': None}
-
-
-@pytest.mark.sphinx('html', testroot='ext-autodoc')
-@pytest.mark.filterwarnings('ignore:autodoc_default_flags is now deprecated.')
-def test_merge_autodoc_default_flags2(app):
-    app.config.autodoc_default_flags = ['members', 'undoc-members']
-    app.config.autodoc_default_options = {'members': 'this,that,order',
-                                          'inherited-members': 'this'}
-    merge_autodoc_default_flags(app, app.config)
-    assert app.config.autodoc_default_options == {'members': None,
-                                                  'undoc-members': None,
-                                                  'inherited-members': 'this'}
-
-
 @pytest.mark.sphinx('html', testroot='ext-autodoc')
 def test_autodoc_default_options(app):
     # no settings
diff --git a/tests/test_ext_autodoc_mock.py b/tests/test_ext_autodoc_mock.py
index 767232bcc..79a2782d3 100644
--- a/tests/test_ext_autodoc_mock.py
+++ b/tests/test_ext_autodoc_mock.py
@@ -17,7 +17,7 @@ from sphinx.ext.autodoc.mock import _MockModule, _MockObject, mock
 
 
 def test_MockModule():
-    mock = _MockModule('mocked_module', None)
+    mock = _MockModule('mocked_module')
     assert isinstance(mock.some_attr, _MockObject)
     assert isinstance(mock.some_method, _MockObject)
     assert isinstance(mock.attr1.attr2, _MockObject)
diff --git a/tests/test_util_images.py b/tests/test_util_images.py
index 5e0f2801c..dbe155035 100644
--- a/tests/test_util_images.py
+++ b/tests/test_util_images.py
@@ -20,20 +20,15 @@ PDF_FILENAME = 'img.pdf'
 TXT_FILENAME = 'index.txt'
 
 
-@pytest.fixture(scope='module')
-def testroot(rootdir):
-    return rootdir / 'test-root'
-
-
-def test_get_image_size(testroot):
-    assert get_image_size(testroot / GIF_FILENAME) == (200, 181)
-    assert get_image_size(testroot / PNG_FILENAME) == (200, 181)
-    assert get_image_size(testroot / PDF_FILENAME) is None
-    assert get_image_size(testroot / TXT_FILENAME) is None
+def test_get_image_size(rootdir):
+    assert get_image_size(rootdir / 'test-root' / GIF_FILENAME) == (200, 181)
+    assert get_image_size(rootdir / 'test-root' / PNG_FILENAME) == (200, 181)
+    assert get_image_size(rootdir / 'test-root' / PDF_FILENAME) is None
+    assert get_image_size(rootdir / 'test-root' / TXT_FILENAME) is None
 
 
 @pytest.mark.filterwarnings('ignore:The content argument')
-def test_guess_mimetype(testroot):
+def test_guess_mimetype():
     # guess by filename
     assert guess_mimetype('img.png') == 'image/png'
     assert guess_mimetype('img.jpg') == 'image/jpeg'
@@ -42,24 +37,9 @@ def test_guess_mimetype(testroot):
     assert guess_mimetype('no_extension') is None
     assert guess_mimetype('IMG.PNG') == 'image/png'
 
-    # guess by content
-    assert guess_mimetype(content=(testroot / GIF_FILENAME).bytes()) == 'image/gif'
-    assert guess_mimetype(content=(testroot / PNG_FILENAME).bytes()) == 'image/png'
-    assert guess_mimetype(content=(testroot / PDF_FILENAME).bytes()) is None
-    assert guess_mimetype(content=(testroot / TXT_FILENAME).bytes()) is None
-    assert guess_mimetype(content=(testroot / TXT_FILENAME).bytes(),
-                          default='text/plain') == 'text/plain'
-
-    # the priority of params: filename > content > default
-    assert guess_mimetype('img.png',
-                          content=(testroot / GIF_FILENAME).bytes(),
-                          default='text/plain') == 'image/png'
-    assert guess_mimetype('no_extension',
-                          content=(testroot / GIF_FILENAME).bytes(),
-                          default='text/plain') == 'image/gif'
-    assert guess_mimetype('no_extension',
-                          content=(testroot / TXT_FILENAME).bytes(),
-                          default='text/plain') == 'text/plain'
+    # default parameter is used when no extension
+    assert guess_mimetype('img.png', 'text/plain') == 'image/png'
+    assert guess_mimetype('no_extension', 'text/plain') == 'text/plain'
 
 
 def test_get_image_extension():