diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index f56caa1..09e39fe 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -1057,20 +1057,20 @@
             self.assertEqual(x.foo, 42)
             self.assertEqual(x.bar, 'abc')
             self.assertEqual(x.__dict__, {'foo': 42, 'bar': 'abc'})
-        samples = [Any, Union, Tuple, Callable, ClassVar]
+        samples = [Any, Union, Tuple, Callable, ClassVar,
+                   Union[int, str], ClassVar[List], Tuple[int, ...], Callable[[str], bytes]]
         for s in samples:
             for proto in range(pickle.HIGHEST_PROTOCOL + 1):
                 z = pickle.dumps(s, proto)
                 x = pickle.loads(z)
                 self.assertEqual(s, x)
-        more_samples = [List, typing.Iterable, typing.Type]
+        more_samples = [List, typing.Iterable, typing.Type, List[int],
+                        typing.Type[typing.Mapping]]
         for s in more_samples:
             for proto in range(pickle.HIGHEST_PROTOCOL + 1):
                 z = pickle.dumps(s, proto)
                 x = pickle.loads(z)
-                self.assertEqual(repr(s), repr(x))  # TODO: fix this
-                                                # see also comment in test_copy_and_deepcopy
-                                                # the issue is typing/#512
+                self.assertEqual(s, x)
 
     def test_copy_and_deepcopy(self):
         T = TypeVar('T')
@@ -1082,7 +1082,27 @@
                   Union['T', int], List['T'], typing.Mapping['T', int]]
         for t in things + [Any]:
             self.assertEqual(t, copy(t))
-            self.assertEqual(repr(t), repr(deepcopy(t))) # Use repr() because of TypeVars
+            self.assertEqual(t, deepcopy(t))
+
+    def test_immutability_by_copy_and_pickle(self):
+        # Special forms like Union, Any, etc., generic aliases to containers like List,
+        # Mapping, etc., and type variabcles are considered immutable by copy and pickle.
+        global TP, TPB, TPV  # for pickle
+        TP = TypeVar('TP')
+        TPB = TypeVar('TPB', bound=int)
+        TPV = TypeVar('TPV', bytes, str)
+        for X in [TP, TPB, TPV, List, typing.Mapping, ClassVar, typing.Iterable,
+                  Union, Any, Tuple, Callable]:
+            self.assertIs(copy(X), X)
+            self.assertIs(deepcopy(X), X)
+            self.assertIs(pickle.loads(pickle.dumps(X)), X)
+        # Check that local type variables are copyable.
+        TL = TypeVar('TL')
+        TLB = TypeVar('TLB', bound=int)
+        TLV = TypeVar('TLV', bytes, str)
+        for X in [TL, TLB, TLV]:
+            self.assertIs(copy(X), X)
+            self.assertIs(deepcopy(X), X)
 
     def test_copy_generic_instances(self):
         T = TypeVar('T')
diff --git a/Lib/typing.py b/Lib/typing.py
index 56126cf..510574c 100644
--- a/Lib/typing.py
+++ b/Lib/typing.py
@@ -285,8 +285,17 @@
         if '_root' not in kwds:
             raise TypeError("Cannot subclass special typing classes")
 
+class _Immutable:
+    """Mixin to indicate that object should not be copied."""
 
-class _SpecialForm(_Final, _root=True):
+    def __copy__(self):
+        return self
+
+    def __deepcopy__(self, memo):
+        return self
+
+
+class _SpecialForm(_Final, _Immutable, _root=True):
     """Internal indicator of special typing constructs.
     See _doc instance attribute for specific docs.
     """
@@ -328,8 +337,8 @@
     def __repr__(self):
         return 'typing.' + self._name
 
-    def __copy__(self):
-        return self  # Special forms are immutable.
+    def __reduce__(self):
+        return self._name
 
     def __call__(self, *args, **kwds):
         raise TypeError(f"Cannot instantiate {self!r}")
@@ -496,7 +505,11 @@
         return f'ForwardRef({self.__forward_arg__!r})'
 
 
-class TypeVar(_Final, _root=True):
+def _find_name(mod, name):
+    return getattr(sys.modules[mod], name)
+
+
+class TypeVar(_Final, _Immutable, _root=True):
     """Type variable.
 
     Usage::
@@ -536,10 +549,12 @@
       T.__covariant__ == False
       T.__contravariant__ = False
       A.__constraints__ == (str, bytes)
+
+    Note that only type variables defined in global scope can be pickled.
     """
 
     __slots__ = ('__name__', '__bound__', '__constraints__',
-                 '__covariant__', '__contravariant__')
+                 '__covariant__', '__contravariant__', '_def_mod')
 
     def __init__(self, name, *constraints, bound=None,
                  covariant=False, contravariant=False):
@@ -558,6 +573,7 @@
             self.__bound__ = _type_check(bound, "Bound must be a type.")
         else:
             self.__bound__ = None
+        self._def_mod = sys._getframe(1).f_globals['__name__']  # for pickling
 
     def __getstate__(self):
         return {'name': self.__name__,
@@ -582,6 +598,9 @@
             prefix = '~'
         return prefix + self.__name__
 
+    def __reduce__(self):
+        return (_find_name, (self._def_mod, self.__name__))
+
 
 # Special typing constructs Union, Optional, Generic, Callable and Tuple
 # use three special attributes for internal bookkeeping of generic types:
@@ -724,6 +743,11 @@
         raise TypeError("Subscripted generics cannot be used with"
                         " class and instance checks")
 
+    def __reduce__(self):
+        if self._special:
+            return self._name
+        return super().__reduce__()
+
 
 class _VariadicGenericAlias(_GenericAlias, _root=True):
     """Same as _GenericAlias above but for variadic aliases. Currently,