diff --git a/CHANGES b/CHANGES
index 22638f6aa..0dd0a4f21 100644
--- a/CHANGES
+++ b/CHANGES
@@ -73,6 +73,8 @@ Features added
   :rst:dir:`py:exception:` and :rst:dir:`py:method:` directives
 * #7596: py domain: Change a type annotation for variables to a hyperlink
 * #7582: napoleon: a type for attribute are represented like type annotation
+* #7683: Add ``allowed_exceptions`` parameter to ``Sphinx.emit()`` to allow
+  handlers to raise specified exceptions
 
 Bugs fixed
 ----------
diff --git a/sphinx/application.py b/sphinx/application.py
index 8f06bf9cf..b02fb4d60 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -436,22 +436,32 @@ class Sphinx:
         logger.debug('[app] disconnecting event: [id=%s]', listener_id)
         self.events.disconnect(listener_id)
 
-    def emit(self, event: str, *args: Any) -> List:
+    def emit(self, event: str, *args: Any,
+             allowed_exceptions: Tuple["Type[Exception]", ...] = ()) -> List:
         """Emit *event* and pass *arguments* to the callback functions.
 
         Return the return values of all callbacks as a list.  Do not emit core
         Sphinx events in extensions!
-        """
-        return self.events.emit(event, *args)
 
-    def emit_firstresult(self, event: str, *args: Any) -> Any:
+        .. versionchanged:: 3.1
+
+           Added *allowed_exceptions* to specify path-through exceptions
+        """
+        return self.events.emit(event, *args, allowed_exceptions=allowed_exceptions)
+
+    def emit_firstresult(self, event: str, *args: Any,
+                         allowed_exceptions: Tuple["Type[Exception]", ...] = ()) -> Any:
         """Emit *event* and pass *arguments* to the callback functions.
 
         Return the result of the first callback that doesn't return ``None``.
 
         .. versionadded:: 0.5
+        .. versionchanged:: 3.1
+
+           Added *allowed_exceptions* to specify path-through exceptions
         """
-        return self.events.emit_firstresult(event, *args)
+        return self.events.emit_firstresult(event, *args,
+                                            allowed_exceptions=allowed_exceptions)
 
     # registering addon parts
 
diff --git a/sphinx/events.py b/sphinx/events.py
index 0f0f47b65..0911dfaaa 100644
--- a/sphinx/events.py
+++ b/sphinx/events.py
@@ -13,7 +13,7 @@
 import warnings
 from collections import defaultdict
 from operator import attrgetter
-from typing import Any, Callable, Dict, List, NamedTuple
+from typing import Any, Callable, Dict, List, NamedTuple, Tuple
 
 from sphinx.deprecation import RemovedInSphinx40Warning
 from sphinx.errors import ExtensionError, SphinxError
@@ -22,6 +22,7 @@ from sphinx.util import logging
 
 if False:
     # For type annotation
+    from typing import Type  # for python3.5.1
     from sphinx.application import Sphinx
 
 
@@ -88,7 +89,8 @@ class EventManager:
                 if listener.id == listener_id:
                     listeners.remove(listener)
 
-    def emit(self, name: str, *args: Any) -> List:
+    def emit(self, name: str, *args: Any,
+             allowed_exceptions: Tuple["Type[Exception]", ...] = ()) -> List:
         """Emit a Sphinx event."""
         try:
             logger.debug('[app] emitting event: %r%s', name, repr(args)[:100])
@@ -106,6 +108,9 @@ class EventManager:
                     results.append(listener.handler(*args))
                 else:
                     results.append(listener.handler(self.app, *args))
+            except allowed_exceptions:
+                # pass through the errors specified as *allowed_exceptions*
+                raise
             except SphinxError:
                 raise
             except Exception as exc:
@@ -113,12 +118,13 @@ class EventManager:
                                      (listener.handler, name)) from exc
         return results
 
-    def emit_firstresult(self, name: str, *args: Any) -> Any:
+    def emit_firstresult(self, name: str, *args: Any,
+                         allowed_exceptions: Tuple["Type[Exception]", ...] = ()) -> Any:
         """Emit a Sphinx event and returns first result.
 
         This returns the result of the first handler that doesn't return ``None``.
         """
-        for result in self.emit(name, *args):
+        for result in self.emit(name, *args, allowed_exceptions=allowed_exceptions):
             if result is not None:
                 return result
         return None
diff --git a/tests/test_events.py b/tests/test_events.py
index 4881588a4..4fbe03a17 100644
--- a/tests/test_events.py
+++ b/tests/test_events.py
@@ -8,6 +8,9 @@
     :license: BSD, see LICENSE for details.
 """
 
+import pytest
+
+from sphinx.errors import ExtensionError
 from sphinx.events import EventManager
 
 
@@ -22,3 +25,19 @@ def test_event_priority():
 
     events.emit('builder-inited')
     assert result == [3, 1, 2, 5, 4]
+
+
+def test_event_allowed_exceptions():
+    def raise_error(app):
+        raise RuntimeError
+
+    events = EventManager(object())  # pass an dummy object as an app
+    events.connect('builder-inited', raise_error, priority=500)
+
+    # all errors are conveted to ExtensionError
+    with pytest.raises(ExtensionError):
+        events.emit('builder-inited')
+
+    # Allow RuntimeError (pass-through)
+    with pytest.raises(RuntimeError):
+        events.emit('builder-inited', allowed_exceptions=(RuntimeError,))