diff --git a/Lib/test/mod_generics_cache.py b/Lib/test/mod_generics_cache.py
new file mode 100644
index 00000000000000..d9a60b4b28c325
--- /dev/null
+++ b/Lib/test/mod_generics_cache.py
@@ -0,0 +1,14 @@
+"""Module for testing the behavior of generics across different modules."""
+
+from typing import TypeVar, Generic
+
+T = TypeVar('T')
+
+
+class A(Generic[T]):
+    pass
+
+
+class B(Generic[T]):
+    class A(Generic[T]):
+        pass
diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index fce6b5aaffdf93..64d8276658ee7f 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -190,6 +190,10 @@ def test_bound_errors(self):
         with self.assertRaises(TypeError):
             TypeVar('X', str, float, bound=Employee)
 
+    def test_no_bivariant(self):
+        with self.assertRaises(ValueError):
+            TypeVar('T', covariant=True, contravariant=True)
+
 
 class UnionTests(BaseTestCase):
 
@@ -254,6 +258,11 @@ def test_repr(self):
         self.assertEqual(repr(u), 'typing.Union[%s.Employee, int]' % __name__)
         u = Union[int, Employee]
         self.assertEqual(repr(u), 'typing.Union[int, %s.Employee]' % __name__)
+        T = TypeVar('T')
+        u = Union[T, int][int]
+        self.assertEqual(repr(u), repr(int))
+        u = Union[List[int], int]
+        self.assertEqual(repr(u), 'typing.Union[typing.List[int], int]')
 
     def test_cannot_subclass(self):
         with self.assertRaises(TypeError):
@@ -304,6 +313,15 @@ def test_union_instance_type_error(self):
         with self.assertRaises(TypeError):
             isinstance(42, Union[int, str])
 
+    def test_no_eval_union(self):
+        u = Union[int, str]
+        def f(x: u): ...
+        self.assertIs(get_type_hints(f)['x'], u)
+
+    def test_function_repr_union(self):
+        def fun() -> int: ...
+        self.assertEqual(repr(Union[fun, int]), 'typing.Union[fun, int]')
+
     def test_union_str_pattern(self):
         # Shouldn't crash; see http://bugs.python.org/issue25390
         A = Union[str, Pattern]
@@ -401,6 +419,8 @@ def test_callable_wrong_forms(self):
             Callable[[()], int]
         with self.assertRaises(TypeError):
             Callable[[int, 1], 2]
+        with self.assertRaises(TypeError):
+            Callable[int]
 
     def test_callable_instance_works(self):
         def f():
@@ -546,15 +566,27 @@ def test_basics(self):
         Y[str]
         with self.assertRaises(TypeError):
             Y[str, str]
+        self.assertIsSubclass(SimpleMapping[str, int], SimpleMapping)
 
     def test_generic_errors(self):
         T = TypeVar('T')
+        S = TypeVar('S')
         with self.assertRaises(TypeError):
             Generic[T]()
+        with self.assertRaises(TypeError):
+            Generic[T][T]
+        with self.assertRaises(TypeError):
+            Generic[T][S]
         with self.assertRaises(TypeError):
             isinstance([], List[int])
         with self.assertRaises(TypeError):
             issubclass(list, List[int])
+        with self.assertRaises(TypeError):
+            class NewGeneric(Generic): ...
+        with self.assertRaises(TypeError):
+            class MyGeneric(Generic[T], Generic[S]): ...
+        with self.assertRaises(TypeError):
+            class MyGeneric(List[T], Generic[S]): ...
 
     def test_init(self):
         T = TypeVar('T')
@@ -738,6 +770,53 @@ def test_subscript_meta(self):
         self.assertEqual(Union[T, int][GenericMeta], Union[GenericMeta, int])
         self.assertEqual(Callable[..., GenericMeta].__args__, (Ellipsis, GenericMeta))
 
+    def test_generic_hashes(self):
+        try:
+            from test import mod_generics_cache
+        except ImportError:  # for Python 3.4 and previous versions
+            import mod_generics_cache
+        class A(Generic[T]):
+            ...
+
+        class B(Generic[T]):
+            class A(Generic[T]):
+                ...
+
+        self.assertEqual(A, A)
+        self.assertEqual(mod_generics_cache.A[str], mod_generics_cache.A[str])
+        self.assertEqual(B.A, B.A)
+        self.assertEqual(mod_generics_cache.B.A[B.A[str]],
+                         mod_generics_cache.B.A[B.A[str]])
+
+        self.assertNotEqual(A, B.A)
+        self.assertNotEqual(A, mod_generics_cache.A)
+        self.assertNotEqual(A, mod_generics_cache.B.A)
+        self.assertNotEqual(B.A, mod_generics_cache.A)
+        self.assertNotEqual(B.A, mod_generics_cache.B.A)
+
+        self.assertNotEqual(A[str], B.A[str])
+        self.assertNotEqual(A[List[Any]], B.A[List[Any]])
+        self.assertNotEqual(A[str], mod_generics_cache.A[str])
+        self.assertNotEqual(A[str], mod_generics_cache.B.A[str])
+        self.assertNotEqual(B.A[int], mod_generics_cache.A[int])
+        self.assertNotEqual(B.A[List[Any]], mod_generics_cache.B.A[List[Any]])
+
+        self.assertNotEqual(Tuple[A[str]], Tuple[B.A[str]])
+        self.assertNotEqual(Tuple[A[List[Any]]], Tuple[B.A[List[Any]]])
+        self.assertNotEqual(Union[str, A[str]], Union[str, mod_generics_cache.A[str]])
+        self.assertNotEqual(Union[A[str], A[str]],
+                            Union[A[str], mod_generics_cache.A[str]])
+        self.assertNotEqual(typing.FrozenSet[A[str]],
+                            typing.FrozenSet[mod_generics_cache.B.A[str]])
+
+        if sys.version_info[:2] > (3, 2):
+            self.assertTrue(repr(Tuple[A[str]]).endswith('<locals>.A[str]]'))
+            self.assertTrue(repr(Tuple[B.A[str]]).endswith('<locals>.B.A[str]]'))
+            self.assertTrue(repr(Tuple[mod_generics_cache.A[str]])
+                            .endswith('mod_generics_cache.A[str]]'))
+            self.assertTrue(repr(Tuple[mod_generics_cache.B.A[str]])
+                            .endswith('mod_generics_cache.B.A[str]]'))
+
     def test_extended_generic_rules_eq(self):
         T = TypeVar('T')
         U = TypeVar('U')
@@ -835,6 +914,8 @@ def test_fail_with_bare_generic(self):
             Tuple[Generic[T]]
         with self.assertRaises(TypeError):
             List[typing._Protocol]
+        with self.assertRaises(TypeError):
+            isinstance(1, Generic)
 
     def test_type_erasure_special(self):
         T = TypeVar('T')
@@ -853,6 +934,11 @@ class MyDict(typing.Dict[T, T]): ...
         class MyDef(typing.DefaultDict[str, T]): ...
         self.assertIs(MyDef[int]().__class__, MyDef)
         self.assertIs(MyDef[int]().__orig_class__, MyDef[int])
+        # ChainMap was added in 3.3
+        if sys.version_info >= (3, 3):
+            class MyChain(typing.ChainMap[str, T]): ...
+            self.assertIs(MyChain[int]().__class__, MyChain)
+            self.assertIs(MyChain[int]().__orig_class__, MyChain[int])
 
     def test_all_repr_eq_any(self):
         objs = (getattr(typing, el) for el in typing.__all__)
@@ -1203,6 +1289,19 @@ def test_forwardref_instance_type_error(self):
         with self.assertRaises(TypeError):
             isinstance(42, fr)
 
+    def test_forwardref_subclass_type_error(self):
+        fr = typing._ForwardRef('int')
+        with self.assertRaises(TypeError):
+            issubclass(int, fr)
+
+    def test_forward_equality(self):
+        fr = typing._ForwardRef('int')
+        self.assertEqual(fr, typing._ForwardRef('int'))
+        self.assertNotEqual(List['int'], List[int])
+
+    def test_forward_repr(self):
+        self.assertEqual(repr(List['int']), "typing.List[_ForwardRef('int')]")
+
     def test_union_forward(self):
 
         def foo(a: Union['T']):
@@ -1285,6 +1384,15 @@ def foo(a: 'whatevers') -> {}:
         ith = get_type_hints(C().foo)
         self.assertEqual(ith, {})
 
+    def test_no_type_check_no_bases(self):
+        class C:
+            def meth(self, x: int): ...
+        @no_type_check
+        class D(C):
+            c = C
+        # verify that @no_type_check never affects bases
+        self.assertEqual(get_type_hints(C.meth), {'x': int})
+
     def test_meta_no_type_check(self):
 
         @no_type_check_decorator
@@ -1401,11 +1509,16 @@ class A:
 class B(A):
     x: ClassVar[Optional['B']] = None
     y: int
+    b: int
 class CSub(B):
     z: ClassVar['CSub'] = B()
 class G(Generic[T]):
     lst: ClassVar[List[T]] = []
 
+class NoneAndForward:
+    parent: 'NoneAndForward'
+    meaning: None
+
 class CoolEmployee(NamedTuple):
     name: str
     cool: int
@@ -1419,10 +1532,13 @@ class XMeth(NamedTuple):
     def double(self):
         return 2 * self.x
 
-class XMethBad(NamedTuple):
+class XRepr(NamedTuple):
     x: int
-    def _fields(self):
-        return 'no chance for this'
+    y: int = 1
+    def __str__(self):
+        return f'{self.x} -> {self.y}'
+    def __add__(self, other):
+        return 0
 """
 
 if PY36:
@@ -1431,7 +1547,7 @@ def _fields(self):
     # fake names for the sake of static analysis
     ann_module = ann_module2 = ann_module3 = None
     A = B = CSub = G = CoolEmployee = CoolEmployeeWithDefault = object
-    XMeth = XMethBad = object
+    XMeth = XRepr = NoneAndForward = object
 
 gth = get_type_hints
 
@@ -1466,6 +1582,8 @@ def test_get_type_hints_classes(self):
                          {'y': Optional[ann_module.C]})
         self.assertEqual(gth(ann_module.S), {'x': str, 'y': str})
         self.assertEqual(gth(ann_module.foo), {'x': int})
+        self.assertEqual(gth(NoneAndForward, globals()),
+                         {'parent': NoneAndForward, 'meaning': type(None)})
 
     @skipUnless(PY36, 'Python 3.6 required')
     def test_respect_no_type_check(self):
@@ -1482,17 +1600,22 @@ def meth(x: int): ...
         class Der(ABase): ...
         self.assertEqual(gth(ABase.meth), {'x': int})
 
-    def test_get_type_hints_for_builins(self):
+    def test_get_type_hints_for_builtins(self):
         # Should not fail for built-in classes and functions.
         self.assertEqual(gth(int), {})
         self.assertEqual(gth(type), {})
         self.assertEqual(gth(dir), {})
         self.assertEqual(gth(len), {})
+        self.assertEqual(gth(object.__str__), {})
+        self.assertEqual(gth(object().__str__), {})
+        self.assertEqual(gth(str.join), {})
 
     def test_previous_behavior(self):
         def testf(x, y): ...
         testf.__annotations__['x'] = 'int'
         self.assertEqual(gth(testf), {'x': int})
+        def testg(x: None): ...
+        self.assertEqual(gth(testg), {'x': type(None)})
 
     def test_get_type_hints_for_object_with_annotations(self):
         class A: ...
@@ -1506,9 +1629,10 @@ def test_get_type_hints_ClassVar(self):
         self.assertEqual(gth(ann_module2.CV, ann_module2.__dict__),
                          {'var': typing.ClassVar[ann_module2.CV]})
         self.assertEqual(gth(B, globals()),
-                         {'y': int, 'x': ClassVar[Optional[B]]})
+                         {'y': int, 'x': ClassVar[Optional[B]], 'b': int})
         self.assertEqual(gth(CSub, globals()),
-                         {'z': ClassVar[CSub], 'y': int, 'x': ClassVar[Optional[B]]})
+                         {'z': ClassVar[CSub], 'y': int, 'b': int,
+                          'x': ClassVar[Optional[B]]})
         self.assertEqual(gth(G), {'lst': ClassVar[List[T]]})
 
 
@@ -1628,6 +1752,11 @@ def test_list(self):
 
     def test_deque(self):
         self.assertIsSubclass(collections.deque, typing.Deque)
+        class MyDeque(typing.Deque[int]): ...
+        self.assertIsInstance(MyDeque(), collections.deque)
+
+    def test_counter(self):
+        self.assertIsSubclass(collections.Counter, typing.Counter)
 
     def test_set(self):
         self.assertIsSubclass(set, typing.Set)
@@ -1680,13 +1809,10 @@ class MyDict(typing.Dict[str, int]):
         self.assertIsSubclass(MyDict, dict)
         self.assertNotIsSubclass(dict, MyDict)
 
-    def test_no_defaultdict_instantiation(self):
-        with self.assertRaises(TypeError):
-            typing.DefaultDict()
-        with self.assertRaises(TypeError):
-            typing.DefaultDict[KT, VT]()
-        with self.assertRaises(TypeError):
-            typing.DefaultDict[str, int]()
+    def test_defaultdict_instantiation(self):
+        self.assertIs(type(typing.DefaultDict()), collections.defaultdict)
+        self.assertIs(type(typing.DefaultDict[KT, VT]()), collections.defaultdict)
+        self.assertIs(type(typing.DefaultDict[str, int]()), collections.defaultdict)
 
     def test_defaultdict_subclass(self):
 
@@ -1699,13 +1825,49 @@ class MyDefDict(typing.DefaultDict[str, int]):
         self.assertIsSubclass(MyDefDict, collections.defaultdict)
         self.assertNotIsSubclass(collections.defaultdict, MyDefDict)
 
-    def test_no_deque_instantiation(self):
-        with self.assertRaises(TypeError):
-            typing.Deque()
-        with self.assertRaises(TypeError):
-            typing.Deque[T]()
-        with self.assertRaises(TypeError):
-            typing.Deque[int]()
+    @skipUnless(sys.version_info >= (3, 3), 'ChainMap was added in 3.3')
+    def test_chainmap_instantiation(self):
+        self.assertIs(type(typing.ChainMap()), collections.ChainMap)
+        self.assertIs(type(typing.ChainMap[KT, VT]()), collections.ChainMap)
+        self.assertIs(type(typing.ChainMap[str, int]()), collections.ChainMap)
+        class CM(typing.ChainMap[KT, VT]): ...
+        self.assertIs(type(CM[int, str]()), CM)
+
+    @skipUnless(sys.version_info >= (3, 3), 'ChainMap was added in 3.3')
+    def test_chainmap_subclass(self):
+
+        class MyChainMap(typing.ChainMap[str, int]):
+            pass
+
+        cm = MyChainMap()
+        self.assertIsInstance(cm, MyChainMap)
+
+        self.assertIsSubclass(MyChainMap, collections.ChainMap)
+        self.assertNotIsSubclass(collections.ChainMap, MyChainMap)
+
+    def test_deque_instantiation(self):
+        self.assertIs(type(typing.Deque()), collections.deque)
+        self.assertIs(type(typing.Deque[T]()), collections.deque)
+        self.assertIs(type(typing.Deque[int]()), collections.deque)
+        class D(typing.Deque[T]): ...
+        self.assertIs(type(D[int]()), D)
+
+    def test_counter_instantiation(self):
+        self.assertIs(type(typing.Counter()), collections.Counter)
+        self.assertIs(type(typing.Counter[T]()), collections.Counter)
+        self.assertIs(type(typing.Counter[int]()), collections.Counter)
+        class C(typing.Counter[T]): ...
+        self.assertIs(type(C[int]()), C)
+
+    def test_counter_subclass_instantiation(self):
+
+        class MyCounter(typing.Counter[int]):
+            pass
+
+        d = MyCounter()
+        self.assertIsInstance(d, MyCounter)
+        self.assertIsInstance(d, typing.Counter)
+        self.assertIsInstance(d, collections.Counter)
 
     def test_no_set_instantiation(self):
         with self.assertRaises(TypeError):
@@ -2018,6 +2180,14 @@ def test_basics(self):
                          collections.OrderedDict([('name', str), ('id', int)]))
         self.assertIs(Emp._field_types, Emp.__annotations__)
 
+    def test_namedtuple_pyversion(self):
+        if sys.version_info[:2] < (3, 6):
+            with self.assertRaises(TypeError):
+                NamedTuple('Name', one=int, other=str)
+            with self.assertRaises(TypeError):
+                class NotYet(NamedTuple):
+                    whatever = 0
+
     @skipUnless(PY36, 'Python 3.6 required')
     def test_annotation_usage(self):
         tim = CoolEmployee('Tim', 9000)
@@ -2055,10 +2225,18 @@ class NonDefaultAfterDefault(NamedTuple):
 
     @skipUnless(PY36, 'Python 3.6 required')
     def test_annotation_usage_with_methods(self):
-        self.assertEquals(XMeth(1).double(), 2)
-        self.assertEquals(XMeth(42).x, XMeth(42)[0])
-        self.assertEquals(XMethBad(1)._fields, ('x',))
-        self.assertEquals(XMethBad(1).__annotations__, {'x': int})
+        self.assertEqual(XMeth(1).double(), 2)
+        self.assertEqual(XMeth(42).x, XMeth(42)[0])
+        self.assertEqual(str(XRepr(42)), '42 -> 1')
+        self.assertEqual(XRepr(1, 2) + XRepr(3), 0)
+
+        with self.assertRaises(AttributeError):
+            exec("""
+class XMethBad(NamedTuple):
+    x: int
+    def _fields(self):
+        return 'no chance for this'
+""")
 
     @skipUnless(PY36, 'Python 3.6 required')
     def test_namedtuple_keyword_usage(self):
@@ -2138,6 +2316,12 @@ def test_basics(self):
         Pattern[Union[str, bytes]]
         Match[Union[bytes, str]]
 
+    def test_alias_equality(self):
+        self.assertEqual(Pattern[str], Pattern[str])
+        self.assertNotEqual(Pattern[str], Pattern[bytes])
+        self.assertNotEqual(Pattern[str], Match[str])
+        self.assertNotEqual(Pattern[str], str)
+
     def test_errors(self):
         with self.assertRaises(TypeError):
             # Doesn't fit AnyStr.
@@ -2152,6 +2336,9 @@ def test_errors(self):
         with self.assertRaises(TypeError):
             # We don't support isinstance().
             isinstance(42, Pattern[str])
+        with self.assertRaises(TypeError):
+            # We don't support issubclass().
+            issubclass(Pattern[bytes], Pattern[str])
 
     def test_repr(self):
         self.assertEqual(repr(Pattern), 'Pattern[~AnyStr]')
diff --git a/Lib/typing.py b/Lib/typing.py
index c9e341753769e0..efe358faf20988 100644
--- a/Lib/typing.py
+++ b/Lib/typing.py
@@ -10,6 +10,12 @@
     import collections.abc as collections_abc
 except ImportError:
     import collections as collections_abc  # Fallback for PY3.2.
+try:
+    from types import SlotWrapperType, MethodWrapperType, MethodDescriptorType
+except ImportError:
+    SlotWrapperType = type(object.__init__)
+    MethodWrapperType = type(object().__str__)
+    MethodDescriptorType = type(str.join)
 
 
 # Please keep __all__ alphabetized within each category.
@@ -62,6 +68,7 @@
     'SupportsRound',
 
     # Concrete collection types.
+    'Counter',
     'Deque',
     'Dict',
     'DefaultDict',
@@ -849,19 +856,6 @@ def _next_in_mro(cls):
     return next_in_mro
 
 
-def _valid_for_check(cls):
-    """An internal helper to prohibit isinstance([1], List[str]) etc."""
-    if cls is Generic:
-        raise TypeError("Class %r cannot be used with class "
-                        "or instance checks" % cls)
-    if (
-        cls.__origin__ is not None and
-        sys._getframe(3).f_globals['__name__'] not in ['abc', 'functools']
-    ):
-        raise TypeError("Parameterized generics cannot be used with class "
-                        "or instance checks")
-
-
 def _make_subclasshook(cls):
     """Construct a __subclasshook__ callable that incorporates
     the associated __extra__ class in subclass checks performed
@@ -872,7 +866,6 @@ def _make_subclasshook(cls):
         # Registered classes need not be checked here because
         # cls and its extra share the same _abc_registry.
         def __extrahook__(subclass):
-            _valid_for_check(cls)
             res = cls.__extra__.__subclasshook__(subclass)
             if res is not NotImplemented:
                 return res
@@ -887,7 +880,6 @@ def __extrahook__(subclass):
     else:
         # For non-ABC extras we'll just call issubclass().
         def __extrahook__(subclass):
-            _valid_for_check(cls)
             if cls.__extra__ and issubclass(subclass, cls.__extra__):
                 return True
             return NotImplemented
@@ -974,6 +966,7 @@ def __new__(cls, name, bases, namespace,
         # remove bare Generic from bases if there are other generic bases
         if any(isinstance(b, GenericMeta) and b is not Generic for b in bases):
             bases = tuple(b for b in bases if b is not Generic)
+        namespace.update({'__origin__': origin, '__extra__': extra})
         self = super().__new__(cls, name, bases, namespace, _root=True)
 
         self.__parameters__ = tvars
@@ -982,8 +975,6 @@ def __new__(cls, name, bases, namespace,
         self.__args__ = tuple(... if a is _TypingEllipsis else
                               () if a is _TypingEmpty else
                               a for a in args) if args else None
-        self.__origin__ = origin
-        self.__extra__ = extra
         # Speed hack (https://github.com/python/typing/issues/196).
         self.__next_in_mro__ = _next_in_mro(self)
         # Preserve base classes on subclassing (__bases__ are type erased now).
@@ -994,20 +985,56 @@ def __new__(cls, name, bases, namespace,
         # with issubclass() and isinstance() in the same way as their
         # collections.abc counterparts (e.g., isinstance([], Iterable)).
         if (
-            # allow overriding
             '__subclasshook__' not in namespace and extra or
-            hasattr(self.__subclasshook__, '__name__') and
-            self.__subclasshook__.__name__ == '__extrahook__'
+            # allow overriding
+            getattr(self.__subclasshook__, '__name__', '') == '__extrahook__'
         ):
             self.__subclasshook__ = _make_subclasshook(self)
         if isinstance(extra, abc.ABCMeta):
             self._abc_registry = extra._abc_registry
+            self._abc_cache = extra._abc_cache
+        elif origin is not None:
+            self._abc_registry = origin._abc_registry
+            self._abc_cache = origin._abc_cache
 
         if origin and hasattr(origin, '__qualname__'):  # Fix for Python 3.2.
             self.__qualname__ = origin.__qualname__
-        self.__tree_hash__ = hash(self._subs_tree()) if origin else hash((self.__name__,))
+        self.__tree_hash__ = (hash(self._subs_tree()) if origin else
+                              super(GenericMeta, self).__hash__())
         return self
 
+    # _abc_negative_cache and _abc_negative_cache_version
+    # realised as descriptors, since GenClass[t1, t2, ...] always
+    # share subclass info with GenClass.
+    # This is an important memory optimization.
+    @property
+    def _abc_negative_cache(self):
+        if isinstance(self.__extra__, abc.ABCMeta):
+            return self.__extra__._abc_negative_cache
+        return _gorg(self)._abc_generic_negative_cache
+
+    @_abc_negative_cache.setter
+    def _abc_negative_cache(self, value):
+        if self.__origin__ is None:
+            if isinstance(self.__extra__, abc.ABCMeta):
+                self.__extra__._abc_negative_cache = value
+            else:
+                self._abc_generic_negative_cache = value
+
+    @property
+    def _abc_negative_cache_version(self):
+        if isinstance(self.__extra__, abc.ABCMeta):
+            return self.__extra__._abc_negative_cache_version
+        return _gorg(self)._abc_generic_negative_cache_version
+
+    @_abc_negative_cache_version.setter
+    def _abc_negative_cache_version(self, value):
+        if self.__origin__ is None:
+            if isinstance(self.__extra__, abc.ABCMeta):
+                self.__extra__._abc_negative_cache_version = value
+            else:
+                self._abc_generic_negative_cache_version = value
+
     def _get_type_vars(self, tvars):
         if self.__origin__ and self.__parameters__:
             _get_type_vars(self.__parameters__, tvars)
@@ -1095,8 +1122,10 @@ def __getitem__(self, params):
             _check_generic(self, params)
             tvars = _type_vars(params)
             args = params
+
+        prepend = (self,) if self.__origin__ is None else ()
         return self.__class__(self.__name__,
-                              self.__bases__,
+                              prepend + self.__bases__,
                               _no_slots_copy(self.__dict__),
                               tvars=tvars,
                               args=args,
@@ -1104,6 +1133,17 @@ def __getitem__(self, params):
                               extra=self.__extra__,
                               orig_bases=self.__orig_bases__)
 
+    def __subclasscheck__(self, cls):
+        if self.__origin__ is not None:
+            if sys._getframe(1).f_globals['__name__'] not in ['abc', 'functools']:
+                raise TypeError("Parameterized generics cannot be used with class "
+                                "or instance checks")
+            return False
+        if self is Generic:
+            raise TypeError("Class %r cannot be used with class "
+                            "or instance checks" % self)
+        return super().__subclasscheck__(cls)
+
     def __instancecheck__(self, instance):
         # Since we extend ABC.__subclasscheck__ and
         # ABC.__instancecheck__ inlines the cache checking done by the
@@ -1398,6 +1438,11 @@ def _get_defaults(func):
     return res
 
 
+_allowed_types = (types.FunctionType, types.BuiltinFunctionType,
+                  types.MethodType, types.ModuleType,
+                  SlotWrapperType, MethodWrapperType, MethodDescriptorType)
+
+
 def get_type_hints(obj, globalns=None, localns=None):
     """Return type hints for an object.
 
@@ -1452,12 +1497,7 @@ def get_type_hints(obj, globalns=None, localns=None):
     hints = getattr(obj, '__annotations__', None)
     if hints is None:
         # Return empty annotations for something that _could_ have them.
-        if (
-            isinstance(obj, types.FunctionType) or
-            isinstance(obj, types.BuiltinFunctionType) or
-            isinstance(obj, types.MethodType) or
-            isinstance(obj, types.ModuleType)
-        ):
+        if isinstance(obj, _allowed_types):
             return {}
         else:
             raise TypeError('{!r} is not a module, class, method, '
@@ -1824,8 +1864,7 @@ class Deque(collections.deque, MutableSequence[T], extra=collections.deque):
 
     def __new__(cls, *args, **kwds):
         if _geqv(cls, Deque):
-            raise TypeError("Type Deque cannot be instantiated; "
-                            "use deque() instead")
+            return collections.deque(*args, **kwds)
         return _generic_new(collections.deque, cls, *args, **kwds)
 
 
@@ -1894,11 +1933,35 @@ class DefaultDict(collections.defaultdict, MutableMapping[KT, VT],
 
     def __new__(cls, *args, **kwds):
         if _geqv(cls, DefaultDict):
-            raise TypeError("Type DefaultDict cannot be instantiated; "
-                            "use collections.defaultdict() instead")
+            return collections.defaultdict(*args, **kwds)
         return _generic_new(collections.defaultdict, cls, *args, **kwds)
 
 
+class Counter(collections.Counter, Dict[T, int], extra=collections.Counter):
+
+    __slots__ = ()
+
+    def __new__(cls, *args, **kwds):
+        if _geqv(cls, Counter):
+            return collections.Counter(*args, **kwds)
+        return _generic_new(collections.Counter, cls, *args, **kwds)
+
+
+if hasattr(collections, 'ChainMap'):
+    # ChainMap only exists in 3.3+
+    __all__.append('ChainMap')
+
+    class ChainMap(collections.ChainMap, MutableMapping[KT, VT],
+                   extra=collections.ChainMap):
+
+        __slots__ = ()
+
+        def __new__(cls, *args, **kwds):
+            if _geqv(cls, ChainMap):
+                return collections.ChainMap(*args, **kwds)
+            return _generic_new(collections.ChainMap, cls, *args, **kwds)
+
+
 # Determine what base class to use for Generator.
 if hasattr(collections_abc, 'Generator'):
     # Sufficiently recent versions of 3.5 have a Generator ABC.
@@ -1975,6 +2038,13 @@ def _make_nmtuple(name, types):
 
 _PY36 = sys.version_info[:2] >= (3, 6)
 
+# attributes prohibited to set in NamedTuple class syntax
+_prohibited = ('__new__', '__init__', '__slots__', '__getnewargs__',
+               '_fields', '_field_defaults', '_field_types',
+               '_make', '_replace', '_asdict')
+
+_special = ('__module__', '__name__', '__qualname__', '__annotations__')
+
 
 class NamedTupleMeta(type):
 
@@ -2002,7 +2072,9 @@ def __new__(cls, typename, bases, ns):
         nm_tpl._field_defaults = defaults_dict
         # update from user namespace without overriding special namedtuple attributes
         for key in ns:
-            if not hasattr(nm_tpl, key):
+            if key in _prohibited:
+                raise AttributeError("Cannot overwrite NamedTuple attribute " + key)
+            elif key not in _special and key not in nm_tpl._fields:
                 setattr(nm_tpl, key, ns[key])
         return nm_tpl
 
diff --git a/Misc/NEWS b/Misc/NEWS
index ceea2226561fd6..0fe1f9b9d651bf 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -59,6 +59,10 @@ Extension Modules
 Library
 -------
 
+- Issue #28556: Various updates to typing module: typing.Counter, typing.ChainMap,
+  improved ABC caching, etc. Original PRs by Jelle Zijlstra, Ivan Levkivskyi,
+  Manuel Krebber, and Łukasz Langa.
+
 - Issue #29100: Fix datetime.fromtimestamp() regression introduced in Python
   3.6.0: check minimum and maximum years.