diff --git a/CHANGES b/CHANGES
index fbfcfd2ab..aa67321dc 100644
--- a/CHANGES
+++ b/CHANGES
@@ -292,6 +292,8 @@ Bugs fixed
 * #3702: LaTeX writer styles figure legends with a hard-coded ``\small``
 * #3708: LaTeX writer allows irc scheme
 * #3717: Stop enforcing that favicon's must be .ico
+* #3731, #3732: Protect isenumclass predicate against non-class arguments
+* #3320: Warning about reference target not being found for container types
 
 Testing
 --------
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 28ea1a08a..eb6fe76cb 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -135,7 +135,7 @@ class PyXrefMixin(object):
         split_contnode = bool(contnode and contnode.astext() == target)
 
         results = []
-        for sub_target in sub_targets:
+        for sub_target in filter(None, sub_targets):
             if split_contnode:
                 contnode = nodes.Text(sub_target)
 
diff --git a/sphinx/util/inspect.py b/sphinx/util/inspect.py
index 2ae31db15..5e0d219ec 100644
--- a/sphinx/util/inspect.py
+++ b/sphinx/util/inspect.py
@@ -142,7 +142,7 @@ def isenumclass(x):
     """Check if the object is subclass of enum."""
     if enum is None:
         return False
-    return issubclass(x, enum.Enum)
+    return inspect.isclass(x) and issubclass(x, enum.Enum)
 
 
 def isenumattribute(x):
diff --git a/tests/roots/test-domain-py/module.rst b/tests/roots/test-domain-py/module.rst
index f3f138639..deb54629e 100644
--- a/tests/roots/test-domain-py/module.rst
+++ b/tests/roots/test-domain-py/module.rst
@@ -29,3 +29,10 @@ module
 .. py:class:: ModTopLevel
 
     * Link to :py:class:`ModNoModule`
+
+.. py:function:: foo(x, y)
+
+   :param x: param x
+   :type  x: int
+   :param y: param y
+   :type  y: tuple(str, float)
diff --git a/tests/test_domain_py.py b/tests/test_domain_py.py
index eb8a7a178..383dd8d33 100644
--- a/tests/test_domain_py.py
+++ b/tests/test_domain_py.py
@@ -109,7 +109,11 @@ def test_domain_py_xrefs(app, status, warning):
                    'ModTopLevel', 'class')
     assert_refnode(refnodes[6], 'module_b.submodule', 'ModTopLevel',
                    'ModNoModule', 'class')
-    assert len(refnodes) == 7
+    assert_refnode(refnodes[7], False, False, 'int', 'obj')
+    assert_refnode(refnodes[8], False, False, 'tuple', 'obj')
+    assert_refnode(refnodes[9], False, False, 'str', 'obj')
+    assert_refnode(refnodes[10], False, False, 'float', 'obj')
+    assert len(refnodes) == 11
 
 
 @pytest.mark.sphinx('dummy', testroot='domain-py')