diff --git a/pydantic/fields.py b/pydantic/fields.py
--- a/pydantic/fields.py
+++ b/pydantic/fields.py
@@ -35,6 +35,7 @@
     Callable,
     ForwardRef,
     NoArgAnyCallable,
+    convert_generics,
     display_as_type,
     get_args,
     get_origin,
@@ -396,7 +397,7 @@ def __init__(
         self.name: str = name
         self.has_alias: bool = bool(alias)
         self.alias: str = alias or name
-        self.type_: Any = type_
+        self.type_: Any = convert_generics(type_)
         self.outer_type_: Any = type_
         self.class_validators = class_validators or {}
         self.default: Any = default
diff --git a/pydantic/typing.py b/pydantic/typing.py
--- a/pydantic/typing.py
+++ b/pydantic/typing.py
@@ -38,6 +38,12 @@
     # python < 3.9 does not have GenericAlias (list[int], tuple[str, ...] and so on)
     TypingGenericAlias = ()
 
+try:
+    from types import UnionType as TypesUnionType  # type: ignore
+except ImportError:
+    # python < 3.10 does not have UnionType (str | int, byte | bool and so on)
+    TypesUnionType = ()
+
 
 if sys.version_info < (3, 9):
 
@@ -145,6 +151,63 @@ def get_args(tp: Type[Any]) -> Tuple[Any, ...]:
         return _typing_get_args(tp) or getattr(tp, '__args__', ()) or _generic_get_args(tp)
 
 
+if sys.version_info < (3, 9):
+
+    def convert_generics(tp: Type[Any]) -> Type[Any]:
+        """Python 3.9 and older only supports generics from `typing` module.
+        They convert strings to ForwardRef automatically.
+
+        Examples::
+            typing.List['Hero'] == typing.List[ForwardRef('Hero')]
+        """
+        return tp
+
+else:
+    from typing import _UnionGenericAlias  # type: ignore
+
+    from typing_extensions import _AnnotatedAlias
+
+    def convert_generics(tp: Type[Any]) -> Type[Any]:
+        """
+        Recursively searches for `str` type hints and replaces them with ForwardRef.
+
+        Examples::
+            convert_generics(list['Hero']) == list[ForwardRef('Hero')]
+            convert_generics(dict['Hero', 'Team']) == dict[ForwardRef('Hero'), ForwardRef('Team')]
+            convert_generics(typing.Dict['Hero', 'Team']) == typing.Dict[ForwardRef('Hero'), ForwardRef('Team')]
+            convert_generics(list[str | 'Hero'] | int) == list[str | ForwardRef('Hero')] | int
+        """
+        origin = get_origin(tp)
+        if not origin or not hasattr(tp, '__args__'):
+            return tp
+
+        args = get_args(tp)
+
+        # typing.Annotated needs special treatment
+        if origin is Annotated:
+            return _AnnotatedAlias(convert_generics(args[0]), args[1:])
+
+        # recursively replace `str` instances inside of `GenericAlias` with `ForwardRef(arg)`
+        converted = tuple(
+            ForwardRef(arg) if isinstance(arg, str) and isinstance(tp, TypingGenericAlias) else convert_generics(arg)
+            for arg in args
+        )
+
+        if converted == args:
+            return tp
+        elif isinstance(tp, TypingGenericAlias):
+            return TypingGenericAlias(origin, converted)
+        elif isinstance(tp, TypesUnionType):
+            # recreate types.UnionType (PEP604, Python >= 3.10)
+            return _UnionGenericAlias(origin, converted)
+        else:
+            try:
+                setattr(tp, '__args__', converted)
+            except AttributeError:
+                pass
+            return tp
+
+
 if sys.version_info < (3, 10):
 
     def is_union(tp: Optional[Type[Any]]) -> bool:

It seems there are two problems, the first one is what you mentioned in the issue, which aparently can be solved by using the legacy types in Typing. I believe that is problematic since PEP 585 was supposed to make list and List equal(at least from my understanding). 

```
from typing import TypedDict, List

from pydantic import BaseModel


class A(TypedDict):
    a: List['A']


class B(BaseModel):
    a: A
```

The problem with this code now becomes a maximum recursion depth. But that's a completly different problem. 
```
...
  File "/home/luccas/Projetos/pydantic/pydantic/typing.py", line 355, in is_literal_type
    return Literal is not None and get_origin(type_) is Literal
  File "/home/luccas/Projetos/pydantic/pydantic/typing.py", line 124, in get_origin
    return _typing_get_origin(tp) or getattr(tp, '__origin__', None)
  File "/usr/lib/python3.9/typing.py", line 1510, in get_origin
    if isinstance(tp, (_BaseGenericAlias, GenericAlias)):
RecursionError: maximum recursion depth exceeded in __instancecheck__
```
This for example works
```
from typing import TypedDict, List
from pydantic import BaseModel


class A(TypedDict):
    foo: int
    bar: str


class B(BaseModel):
    a: List['A']
```

Output of python -c "import pydantic.utils; print(pydantic.utils.version_info())":

```
             pydantic version: 1.8.2
            pydantic compiled: False
                 install path: /home/luccas/Projetos/pydantic/pydantic
               python version: 3.9.7 (default, Aug 31 2021, 13:28:12)  [GCC 11.1.0]
                     platform: Linux-5.4.148-1-MANJARO-x86_64-with-glibc2.33
     optional deps. installed: ['devtools', 'dotenv', 'email-validator', 'typing-extensions']


```

diff --git a/tests/test_forward_ref.py b/tests/test_forward_ref.py
--- a/tests/test_forward_ref.py
+++ b/tests/test_forward_ref.py
@@ -672,6 +672,48 @@ class Config:
     assert m.json(models_as_dict=False) == '{"name": "anne", "friends": ["User(ben)", "User(charlie)"]}'
 
 
+skip_pep585 = pytest.mark.skipif(
+    sys.version_info < (3, 9), reason='PEP585 generics only supported for python 3.9 and above'
+)
+
+
+@skip_pep585
+def test_pep585_self_referencing_generics():
+    class SelfReferencing(BaseModel):
+        names: list['SelfReferencing']  # noqa: F821
+
+    SelfReferencing.update_forward_refs()  # will raise an exception if the forward ref isn't resolvable
+    # test the class
+    assert SelfReferencing.__fields__['names'].type_ is SelfReferencing
+    # NOTE: outer_type_ is not converted
+    assert SelfReferencing.__fields__['names'].outer_type_ == list['SelfReferencing']
+    # test that object creation works
+    obj = SelfReferencing(names=[SelfReferencing(names=[])])
+    assert obj.names == [SelfReferencing(names=[])]
+
+
+@skip_pep585
+def test_pep585_recursive_generics(create_module):
+    @create_module
+    def module():
+        from pydantic import BaseModel
+
+        class Team(BaseModel):
+            name: str
+            heroes: list['Hero']  # noqa: F821
+
+        class Hero(BaseModel):
+            name: str
+            teams: list[Team]
+
+        Team.update_forward_refs()
+
+    assert module.Team.__fields__['heroes'].type_ is module.Hero
+    assert module.Hero.__fields__['teams'].type_ is module.Team
+
+    module.Hero(name='Ivan', teams=[module.Team(name='TheBest', heroes=[])])
+
+
 @pytest.mark.skipif(sys.version_info < (3, 9), reason='needs 3.9 or newer')
 def test_class_var_forward_ref(create_module):
     # see #3679
diff --git a/tests/test_typing.py b/tests/test_typing.py
--- a/tests/test_typing.py
+++ b/tests/test_typing.py
@@ -1,9 +1,12 @@
+import sys
 from collections import namedtuple
-from typing import Callable as TypingCallable, NamedTuple
+from typing import Any, Callable as TypingCallable, Dict, ForwardRef, List, NamedTuple, NewType, Union  # noqa: F401
 
 import pytest
+from typing_extensions import Annotated  # noqa: F401
 
-from pydantic.typing import Literal, is_namedtuple, is_none_type, is_typeddict
+from pydantic import Field  # noqa: F401
+from pydantic.typing import Literal, convert_generics, is_namedtuple, is_none_type, is_typeddict
 
 try:
     from typing import TypedDict as typing_TypedDict
@@ -66,3 +69,58 @@ def test_is_none_type():
     # `collections.abc.Callable` (even with python >= 3.9) as they behave
     # differently
     assert is_none_type(TypingCallable) is False
+
+
+class Hero:
+    pass
+
+
+class Team:
+    pass
+
+
+@pytest.mark.skipif(sys.version_info < (3, 9), reason='PEP585 generics only supported for python 3.9 and above.')
+@pytest.mark.parametrize(
+    ['type_', 'expectations'],
+    [
+        ('int', 'int'),
+        ('Union[list["Hero"], int]', 'Union[list[ForwardRef("Hero")], int]'),
+        ('list["Hero"]', 'list[ForwardRef("Hero")]'),
+        ('dict["Hero", "Team"]', 'dict[ForwardRef("Hero"), ForwardRef("Team")]'),
+        ('dict["Hero", list["Team"]]', 'dict[ForwardRef("Hero"), list[ForwardRef("Team")]]'),
+        ('dict["Hero", List["Team"]]', 'dict[ForwardRef("Hero"), List[ForwardRef("Team")]]'),
+        ('Dict["Hero", list["Team"]]', 'Dict[ForwardRef("Hero"), list[ForwardRef("Team")]]'),
+        (
+            'Annotated[list["Hero"], Field(min_length=2)]',
+            'Annotated[list[ForwardRef("Hero")], Field(min_length=2)]',
+        ),
+    ],
+)
+def test_convert_generics(type_, expectations):
+    assert str(convert_generics(eval(type_))) == str(eval(expectations))
+
+
+@pytest.mark.skipif(sys.version_info < (3, 10), reason='NewType class was added in python 3.10.')
+def test_convert_generics_unsettable_args():
+    class User(NewType):
+
+        __origin__ = type(list[str])
+        __args__ = (list['Hero'],)
+
+        def __init__(self, name: str, tp: type) -> None:
+            super().__init__(name, tp)
+
+        def __setattr__(self, __name: str, __value: Any) -> None:
+            if __name == '__args__':
+                raise AttributeError  # will be thrown during the generics conversion
+            return super().__setattr__(__name, __value)
+
+    # tests that convert_generics will not throw an exception even if __args__ isn't settable
+    assert convert_generics(User('MyUser', str)).__args__ == (list['Hero'],)
+
+
+@pytest.mark.skipif(sys.version_info < (3, 10), reason='PEP604 unions only supported for python 3.10 and above.')
+def test_convert_generics_pep604():
+    assert (
+        convert_generics(dict['Hero', list['Team']] | int) == dict[ForwardRef('Hero'), list[ForwardRef('Team')]] | int
+    )

Recursive list of TypedDicts doesn't work
# Bug

Output of `python -c "import pydantic.utils; print(pydantic.utils.version_info())"`:
```
pydantic version: 1.8
            pydantic compiled: True
                 install path: /usr/local/lib/python3.9/dist-packages/pydantic
               python version: 3.9.6 (default, Jul  3 2021, 17:50:42)  [GCC 7.5.0]
                     platform: Linux-5.4.0-66-generic-x86_64-with-glibc2.27
     optional deps. installed: ['typing-extensions']
```

```py
from typing import TypedDict

from pydantic import BaseModel


class A(TypedDict):
    a: list['A']


class B(BaseModel):
    a: A
```
Result: "RuntimeError: error checking inheritance of 'A' (type: str)"
Adding `from __future__ import annotations` doesn't help


tests/test_forward_ref.py::test_postponed_annotations tests/test_forward_ref.py::test_postponed_annotations_optional tests/test_forward_ref.py::test_postponed_annotations_auto_update_forward_refs tests/test_forward_ref.py::test_forward_ref_auto_update_no_model tests/test_forward_ref.py::test_forward_ref_one_of_fields_not_defined tests/test_forward_ref.py::test_basic_forward_ref tests/test_forward_ref.py::test_self_forward_ref_module tests/test_forward_ref.py::test_self_forward_ref_collection tests/test_forward_ref.py::test_self_forward_ref_local tests/test_forward_ref.py::test_missing_update_forward_refs tests/test_forward_ref.py::test_forward_ref_dataclass tests/test_forward_ref.py::test_forward_ref_dataclass_with_future_annotations tests/test_forward_ref.py::test_forward_ref_sub_types tests/test_forward_ref.py::test_forward_ref_nested_sub_types tests/test_forward_ref.py::test_self_reference_json_schema tests/test_forward_ref.py::test_self_reference_json_schema_with_future_annotations tests/test_forward_ref.py::test_circular_reference_json_schema tests/test_forward_ref.py::test_circular_reference_json_schema_with_future_annotations tests/test_forward_ref.py::test_forward_ref_with_field tests/test_forward_ref.py::test_forward_ref_optional tests/test_forward_ref.py::test_forward_ref_with_create_model tests/test_forward_ref.py::test_resolve_forward_ref_dataclass tests/test_forward_ref.py::test_nested_forward_ref tests/test_forward_ref.py::test_discriminated_union_forward_ref tests/test_forward_ref.py::test_class_var_as_string tests/test_forward_ref.py::test_json_encoder_str tests/test_forward_ref.py::test_json_encoder_forward_ref tests/test_typing.py::test_is_namedtuple tests/test_typing.py::test_is_typeddict_typing[TypedDict0] tests/test_typing.py::test_is_typeddict_typing[TypedDict1] tests/test_typing.py::test_is_none_type