diff --git a/pydantic/schema.py b/pydantic/schema.py
--- a/pydantic/schema.py
+++ b/pydantic/schema.py
@@ -11,6 +11,7 @@
     Callable,
     Dict,
     FrozenSet,
+    Generic,
     Iterable,
     List,
     Optional,
@@ -27,6 +28,7 @@
 
 from .fields import (
     SHAPE_FROZENSET,
+    SHAPE_GENERIC,
     SHAPE_ITERABLE,
     SHAPE_LIST,
     SHAPE_MAPPING,
@@ -481,7 +483,7 @@ def field_type_schema(
             sub_schema = sub_schema[0]  # type: ignore
         f_schema = {'type': 'array', 'items': sub_schema}
     else:
-        assert field.shape == SHAPE_SINGLETON, field.shape
+        assert field.shape in {SHAPE_SINGLETON, SHAPE_GENERIC}, field.shape
         f_schema, f_definitions, f_nested_models = field_singleton_schema(
             field,
             by_alias=by_alias,
@@ -496,7 +498,11 @@ def field_type_schema(
 
     # check field type to avoid repeated calls to the same __modify_schema__ method
     if field.type_ != field.outer_type_:
-        modify_schema = getattr(field.outer_type_, '__modify_schema__', None)
+        if field.shape == SHAPE_GENERIC:
+            field_type = field.type_
+        else:
+            field_type = field.outer_type_
+        modify_schema = getattr(field_type, '__modify_schema__', None)
         if modify_schema:
             modify_schema(f_schema)
     return f_schema, definitions, nested_models
@@ -828,6 +834,11 @@ def field_singleton_schema(  # noqa: C901 (ignore complexity)
         schema_ref = get_schema_ref(model_name, ref_prefix, ref_template, schema_overrides)
         return schema_ref, definitions, nested_models
 
+    # For generics with no args
+    args = get_args(field_type)
+    if args is not None and not args and Generic in field_type.__bases__:
+        return f_schema, definitions, nested_models
+
     raise ValueError(f'Value not declarable with JSON Schema, field: {field}')
 
 
diff --git a/pydantic/typing.py b/pydantic/typing.py
--- a/pydantic/typing.py
+++ b/pydantic/typing.py
@@ -92,7 +92,7 @@ def evaluate_forwardref(type_: ForwardRef, globalns: Any, localns: Any) -> Any:
     if sys.version_info < (3, 7):
 
         def get_args(t: Type[Any]) -> Tuple[Any, ...]:
-            """Simplest get_args compatability layer possible.
+            """Simplest get_args compatibility layer possible.
 
             The Python 3.6 typing module does not have `_GenericAlias` so
             this won't work for everything. In particular this will not
@@ -106,7 +106,7 @@ def get_args(t: Type[Any]) -> Tuple[Any, ...]:
         from typing import _GenericAlias
 
         def get_args(t: Type[Any]) -> Tuple[Any, ...]:
-            """Compatability version of get_args for python 3.7.
+            """Compatibility version of get_args for python 3.7.
 
             Mostly compatible with the python 3.8 `typing` module version
             and able to handle almost all use cases.

Looks to me like generating schema for generic fields just hasn't been implemented yet.

Happy to review and accept a PR to implement this.
diff --git a/tests/test_schema.py b/tests/test_schema.py
--- a/tests/test_schema.py
+++ b/tests/test_schema.py
@@ -7,7 +7,21 @@
 from enum import Enum, IntEnum
 from ipaddress import IPv4Address, IPv4Interface, IPv4Network, IPv6Address, IPv6Interface, IPv6Network
 from pathlib import Path
-from typing import Any, Callable, Dict, FrozenSet, Iterable, List, NewType, Optional, Set, Tuple, Union
+from typing import (
+    Any,
+    Callable,
+    Dict,
+    FrozenSet,
+    Generic,
+    Iterable,
+    List,
+    NewType,
+    Optional,
+    Set,
+    Tuple,
+    TypeVar,
+    Union,
+)
 from uuid import UUID
 
 import pytest
@@ -2149,3 +2163,58 @@ class Model(BaseModel):
         f'{module_2.__name__}__MyEnum',
         f'{module_2.__name__}__MyModel',
     }
+
+
+@pytest.mark.skipif(
+    sys.version_info < (3, 7), reason='schema generation for generic fields is not available in python < 3.7'
+)
+def test_schema_for_generic_field():
+    T = TypeVar('T')
+
+    class GenModel(Generic[T]):
+        def __init__(self, data: Any):
+            self.data = data
+
+        @classmethod
+        def __get_validators__(cls):
+            yield cls.validate
+
+        @classmethod
+        def validate(cls, v: Any):
+            return v
+
+    class Model(BaseModel):
+        data: GenModel[str]
+        data1: GenModel
+
+    assert Model.schema() == {
+        'title': 'Model',
+        'type': 'object',
+        'properties': {
+            'data': {'title': 'Data', 'type': 'string'},
+            'data1': {
+                'title': 'Data1',
+            },
+        },
+        'required': ['data', 'data1'],
+    }
+
+    class GenModelModified(GenModel, Generic[T]):
+        @classmethod
+        def __modify_schema__(cls, field_schema):
+            field_schema.pop('type', None)
+            field_schema.update(anyOf=[{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}])
+
+    class ModelModified(BaseModel):
+        data: GenModelModified[str]
+        data1: GenModelModified
+
+    assert ModelModified.schema() == {
+        'title': 'ModelModified',
+        'type': 'object',
+        'properties': {
+            'data': {'title': 'Data', 'anyOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]},
+            'data1': {'title': 'Data1', 'anyOf': [{'type': 'string'}, {'type': 'array', 'items': {'type': 'string'}}]},
+        },
+        'required': ['data', 'data1'],
+    }

BaseModel.schema() fails when using generic types
# Bug
## Version
Output of `python -c "import pydantic.utils; print(pydantic.utils.version_info())"`:
```
  pydantic version: 1.5.1
            pydantic compiled: True
                 install path: C:\Users\adrian\miniconda3\envs\sangl-butler\Lib\site-packages\pydantic
               python version: 3.8.1 (default, Mar  2 2020, 13:06:26) [MSC v.1916 64 bit (AMD64)]
                     platform: Windows-10-10.0.18362-SP0
     optional deps. installed: ['typing-extensions', 'email-validator']

```
## Description
Hi there!

I want to write a generic type, that behaves like the type it extends, but injects fields into the model with ``__modify_schema__``. So my approach was to use a generic class to use it like that:

```py
from pydantic import BaseModel

class MyModel(BaseModel):
   my_field: FieldThatModifiesModel[str] = "Default value"

````
The field should completely behave like the type var.

However, when I use a generic type in my model, I can't retrieve the model anymore.
See the code below (taken from the docs):
## Example
```py
from pydantic import BaseModel, ValidationError
from pydantic.fields import ModelField
from typing import TypeVar, Generic

AgedType = TypeVar('AgedType')
QualityType = TypeVar('QualityType')

# This is not a pydantic model, it's an arbitrary generic class
class TastingModel(Generic[AgedType, QualityType]):
    def __init__(self, name: str, aged: AgedType, quality: QualityType):
        self.name = name
        self.aged = aged
        self.quality = quality

    @classmethod
    def __get_validators__(cls):
        yield cls.validate

    @classmethod
    # You don't need to add the "ModelField", but it will help your
    # editor give you completion and catch errors
    def validate(cls, v, field: ModelField):
        if not isinstance(v, cls):
            # The value is not even a TastingModel
            raise TypeError('Invalid value')
        if not field.sub_fields:
            # Generic parameters were not provided so we don't try to validate
            # them and just return the value as is
            return v
        aged_f = field.sub_fields[0]
        quality_f = field.sub_fields[1]
        errors = []
        # Here we don't need the validated value, but we want the errors
        valid_value, error = aged_f.validate(v.aged, {}, loc='aged')
        if error:
            errors.append(error)
        # Here we don't need the validated value, but we want the errors
        valid_value, error = quality_f.validate(v.quality, {}, loc='quality')
        if error:
            errors.append(error)
        if errors:
            raise ValidationError(errors, cls)
        # Validation passed without errors, return the same instance received
        return v

class Model(BaseModel):
    # for wine, "aged" is an int with years, "quality" is a float
    wine: TastingModel[int, float]
    # for cheese, "aged" is a bool, "quality" is a str
    cheese: TastingModel[bool, str]
    # for thing, "aged" is a Any, "quality" is Any
    thing: TastingModel

print(Model.schema())
"""
Traceback (most recent call last):
  File ".../generic_type.py", line 54, in <module>
    print(Model.schema())
  File "pydantic\main.py", line 556, in pydantic.main.BaseModel.schema
  File "pydantic\schema.py", line 132, in pydantic.schema.model_schema
  File "pydantic\schema.py", line 455, in pydantic.schema.model_process_schema
  File "pydantic\schema.py", line 491, in pydantic.schema.model_type_schema
  File "pydantic\schema.py", line 185, in pydantic.schema.field_schema
  File "pydantic\schema.py", line 411, in pydantic.schema.field_type_schema
AssertionError: 10
"""
```


tests/test_schema.py::test_schema_for_generic_field
tests/test_schema.py::test_key tests/test_schema.py::test_by_alias tests/test_schema.py::test_ref_template tests/test_schema.py::test_by_alias_generator tests/test_schema.py::test_sub_model tests/test_schema.py::test_schema_class tests/test_schema.py::test_schema_repr tests/test_schema.py::test_schema_class_by_alias tests/test_schema.py::test_choices tests/test_schema.py::test_enum_modify_schema tests/test_schema.py::test_enum_schema_custom_field tests/test_schema.py::test_enum_and_model_have_same_behaviour tests/test_schema.py::test_list_enum_schema_extras tests/test_schema.py::test_json_schema tests/test_schema.py::test_list_sub_model tests/test_schema.py::test_optional tests/test_schema.py::test_any tests/test_schema.py::test_set tests/test_schema.py::test_const_str tests/test_schema.py::test_const_false tests/test_schema.py::test_tuple[tuple-expected_schema0] tests/test_schema.py::test_tuple[field_type1-expected_schema1] tests/test_schema.py::test_tuple[field_type2-expected_schema2] tests/test_schema.py::test_bool tests/test_schema.py::test_strict_bool tests/test_schema.py::test_dict tests/test_schema.py::test_list tests/test_schema.py::test_list_union_dict[field_type0-expected_schema0] tests/test_schema.py::test_list_union_dict[field_type1-expected_schema1] tests/test_schema.py::test_list_union_dict[field_type2-expected_schema2] tests/test_schema.py::test_list_union_dict[field_type3-expected_schema3] tests/test_schema.py::test_list_union_dict[field_type4-expected_schema4] tests/test_schema.py::test_date_types[datetime-expected_schema0] tests/test_schema.py::test_date_types[date-expected_schema1] tests/test_schema.py::test_date_types[time-expected_schema2] tests/test_schema.py::test_date_types[timedelta-expected_schema3] tests/test_schema.py::test_str_basic_types[field_type0-expected_schema0] tests/test_schema.py::test_str_basic_types[field_type1-expected_schema1] tests/test_schema.py::test_str_basic_types[field_type2-expected_schema2] tests/test_schema.py::test_str_basic_types[field_type3-expected_schema3] tests/test_schema.py::test_str_constrained_types[StrictStr-expected_schema0] tests/test_schema.py::test_str_constrained_types[ConstrainedStr-expected_schema1] tests/test_schema.py::test_str_constrained_types[ConstrainedStrValue-expected_schema2] tests/test_schema.py::test_special_str_types[AnyUrl-expected_schema0] tests/test_schema.py::test_special_str_types[UrlValue-expected_schema1] tests/test_schema.py::test_email_str_types[EmailStr-email] tests/test_schema.py::test_email_str_types[NameEmail-name-email] tests/test_schema.py::test_secret_types[SecretBytes-string] tests/test_schema.py::test_secret_types[SecretStr-string] tests/test_schema.py::test_special_int_types[ConstrainedInt-expected_schema0] tests/test_schema.py::test_special_int_types[ConstrainedIntValue-expected_schema1] tests/test_schema.py::test_special_int_types[ConstrainedIntValue-expected_schema2] tests/test_schema.py::test_special_int_types[ConstrainedIntValue-expected_schema3] tests/test_schema.py::test_special_int_types[PositiveInt-expected_schema4] tests/test_schema.py::test_special_int_types[NegativeInt-expected_schema5] tests/test_schema.py::test_special_int_types[NonNegativeInt-expected_schema6] tests/test_schema.py::test_special_int_types[NonPositiveInt-expected_schema7] tests/test_schema.py::test_special_float_types[ConstrainedFloat-expected_schema0] tests/test_schema.py::test_special_float_types[ConstrainedFloatValue-expected_schema1] tests/test_schema.py::test_special_float_types[ConstrainedFloatValue-expected_schema2] tests/test_schema.py::test_special_float_types[ConstrainedFloatValue-expected_schema3] tests/test_schema.py::test_special_float_types[PositiveFloat-expected_schema4] tests/test_schema.py::test_special_float_types[NegativeFloat-expected_schema5] tests/test_schema.py::test_special_float_types[NonNegativeFloat-expected_schema6] tests/test_schema.py::test_special_float_types[NonPositiveFloat-expected_schema7] tests/test_schema.py::test_special_float_types[ConstrainedDecimal-expected_schema8] tests/test_schema.py::test_special_float_types[ConstrainedDecimalValue-expected_schema9] tests/test_schema.py::test_special_float_types[ConstrainedDecimalValue-expected_schema10] tests/test_schema.py::test_special_float_types[ConstrainedDecimalValue-expected_schema11] tests/test_schema.py::test_uuid_types[UUID-uuid] tests/test_schema.py::test_uuid_types[UUID1-uuid1] tests/test_schema.py::test_uuid_types[UUID3-uuid3] tests/test_schema.py::test_uuid_types[UUID4-uuid4] tests/test_schema.py::test_uuid_types[UUID5-uuid5] tests/test_schema.py::test_path_types[FilePath-file-path] tests/test_schema.py::test_path_types[DirectoryPath-directory-path] tests/test_schema.py::test_path_types[Path-path] tests/test_schema.py::test_json_type tests/test_schema.py::test_ipv4address_type tests/test_schema.py::test_ipv6address_type tests/test_schema.py::test_ipvanyaddress_type tests/test_schema.py::test_ipv4interface_type tests/test_schema.py::test_ipv6interface_type tests/test_schema.py::test_ipvanyinterface_type tests/test_schema.py::test_ipv4network_type tests/test_schema.py::test_ipv6network_type tests/test_schema.py::test_ipvanynetwork_type tests/test_schema.py::test_callable_type[annotation0] tests/test_schema.py::test_callable_type[annotation1] tests/test_schema.py::test_error_non_supported_types tests/test_schema.py::test_flat_models_unique_models tests/test_schema.py::test_flat_models_with_submodels tests/test_schema.py::test_flat_models_with_submodels_from_sequence tests/test_schema.py::test_model_name_maps tests/test_schema.py::test_schema_overrides tests/test_schema.py::test_schema_overrides_w_union tests/test_schema.py::test_schema_from_models tests/test_schema.py::test_schema_with_refs[#/components/schemas/-None] tests/test_schema.py::test_schema_with_refs[None-#/components/schemas/{model}] tests/test_schema.py::test_schema_with_refs[#/components/schemas/-#/{model}/schemas/] tests/test_schema.py::test_schema_with_custom_ref_template tests/test_schema.py::test_schema_ref_template_key_error tests/test_schema.py::test_schema_no_definitions tests/test_schema.py::test_list_default tests/test_schema.py::test_dict_default tests/test_schema.py::test_constraints_schema[kwargs0-str-expected_extra0] tests/test_schema.py::test_constraints_schema[kwargs1-ConstrainedStrValue-expected_extra1] tests/test_schema.py::test_constraints_schema[kwargs2-str-expected_extra2] tests/test_schema.py::test_constraints_schema[kwargs3-bytes-expected_extra3] tests/test_schema.py::test_constraints_schema[kwargs4-str-expected_extra4] tests/test_schema.py::test_constraints_schema[kwargs5-int-expected_extra5] tests/test_schema.py::test_constraints_schema[kwargs6-int-expected_extra6] tests/test_schema.py::test_constraints_schema[kwargs7-int-expected_extra7] tests/test_schema.py::test_constraints_schema[kwargs8-int-expected_extra8] tests/test_schema.py::test_constraints_schema[kwargs9-int-expected_extra9] tests/test_schema.py::test_constraints_schema[kwargs10-float-expected_extra10] tests/test_schema.py::test_constraints_schema[kwargs11-float-expected_extra11] tests/test_schema.py::test_constraints_schema[kwargs12-float-expected_extra12] tests/test_schema.py::test_constraints_schema[kwargs13-float-expected_extra13] tests/test_schema.py::test_constraints_schema[kwargs14-float-expected_extra14] tests/test_schema.py::test_constraints_schema[kwargs15-float-expected_extra15] tests/test_schema.py::test_constraints_schema[kwargs16-float-expected_extra16] tests/test_schema.py::test_constraints_schema[kwargs17-float-expected_extra17] tests/test_schema.py::test_constraints_schema[kwargs18-float-expected_extra18] tests/test_schema.py::test_constraints_schema[kwargs19-Decimal-expected_extra19] tests/test_schema.py::test_constraints_schema[kwargs20-Decimal-expected_extra20] tests/test_schema.py::test_constraints_schema[kwargs21-Decimal-expected_extra21] tests/test_schema.py::test_constraints_schema[kwargs22-Decimal-expected_extra22] tests/test_schema.py::test_constraints_schema[kwargs23-Decimal-expected_extra23] tests/test_schema.py::test_unenforced_constraints_schema[kwargs0-int] tests/test_schema.py::test_unenforced_constraints_schema[kwargs1-float] tests/test_schema.py::test_unenforced_constraints_schema[kwargs2-Decimal] tests/test_schema.py::test_unenforced_constraints_schema[kwargs3-int] tests/test_schema.py::test_unenforced_constraints_schema[kwargs4-str] tests/test_schema.py::test_unenforced_constraints_schema[kwargs5-bytes] tests/test_schema.py::test_unenforced_constraints_schema[kwargs6-str] tests/test_schema.py::test_unenforced_constraints_schema[kwargs7-bool] tests/test_schema.py::test_unenforced_constraints_schema[kwargs8-type_8] tests/test_schema.py::test_unenforced_constraints_schema[kwargs9-type_9] tests/test_schema.py::test_unenforced_constraints_schema[kwargs10-ConstrainedListValue] tests/test_schema.py::test_unenforced_constraints_schema[kwargs11-ConstrainedSetValue] tests/test_schema.py::test_constraints_schema_validation[kwargs0-str-foo] tests/test_schema.py::test_constraints_schema_validation[kwargs1-str-foo] tests/test_schema.py::test_constraints_schema_validation[kwargs2-bytes-foo] tests/test_schema.py::test_constraints_schema_validation[kwargs3-str-foo] tests/test_schema.py::test_constraints_schema_validation[kwargs4-int-3] tests/test_schema.py::test_constraints_schema_validation[kwargs5-int-3] tests/test_schema.py::test_constraints_schema_validation[kwargs6-int-3] tests/test_schema.py::test_constraints_schema_validation[kwargs7-int-2] tests/test_schema.py::test_constraints_schema_validation[kwargs8-int-3] tests/test_schema.py::test_constraints_schema_validation[kwargs9-int-3] tests/test_schema.py::test_constraints_schema_validation[kwargs10-int-5] tests/test_schema.py::test_constraints_schema_validation[kwargs11-float-3.0] tests/test_schema.py::test_constraints_schema_validation[kwargs12-float-2.1] tests/test_schema.py::test_constraints_schema_validation[kwargs13-float-3.0] tests/test_schema.py::test_constraints_schema_validation[kwargs14-float-4.9] tests/test_schema.py::test_constraints_schema_validation[kwargs15-float-3.0] tests/test_schema.py::test_constraints_schema_validation[kwargs16-float-2.0] tests/test_schema.py::test_constraints_schema_validation[kwargs17-float-3.0] tests/test_schema.py::test_constraints_schema_validation[kwargs18-float-5.0] tests/test_schema.py::test_constraints_schema_validation[kwargs19-float-3] tests/test_schema.py::test_constraints_schema_validation[kwargs20-float-3] tests/test_schema.py::test_constraints_schema_validation[kwargs21-Decimal-value21] tests/test_schema.py::test_constraints_schema_validation[kwargs22-Decimal-value22] tests/test_schema.py::test_constraints_schema_validation[kwargs23-Decimal-value23] tests/test_schema.py::test_constraints_schema_validation[kwargs24-Decimal-value24] tests/test_schema.py::test_constraints_schema_validation[kwargs25-Decimal-value25] tests/test_schema.py::test_constraints_schema_validation[kwargs26-Decimal-value26] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs0-str-foobar] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs1-str-f] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs2-str-bar] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs3-int-2] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs4-int-5] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs5-int-1] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs6-int-6] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs7-float-2.0] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs8-float-5.0] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs9-float-1.9] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs10-float-5.1] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs11-Decimal-value11] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs12-Decimal-value12] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs13-Decimal-value13] tests/test_schema.py::test_constraints_schema_validation_raises[kwargs14-Decimal-value14] tests/test_schema.py::test_schema_kwargs tests/test_schema.py::test_schema_dict_constr tests/test_schema.py::test_bytes_constrained_types[ConstrainedBytes-expected_schema0] tests/test_schema.py::test_bytes_constrained_types[ConstrainedBytesValue-expected_schema1] tests/test_schema.py::test_optional_dict tests/test_schema.py::test_optional_validator tests/test_schema.py::test_field_with_validator tests/test_schema.py::test_unparameterized_schema_generation tests/test_schema.py::test_known_model_optimization tests/test_schema.py::test_root tests/test_schema.py::test_root_list tests/test_schema.py::test_root_nested_model tests/test_schema.py::test_new_type_schema tests/test_schema.py::test_literal_schema tests/test_schema.py::test_color_type tests/test_schema.py::test_model_with_schema_extra tests/test_schema.py::test_model_with_schema_extra_callable tests/test_schema.py::test_model_with_schema_extra_callable_no_model_class tests/test_schema.py::test_model_with_schema_extra_callable_classmethod tests/test_schema.py::test_model_with_schema_extra_callable_instance_method tests/test_schema.py::test_model_with_extra_forbidden tests/test_schema.py::test_enforced_constraints[int-kwargs0-field_schema0] tests/test_schema.py::test_enforced_constraints[annotation1-kwargs1-field_schema1] tests/test_schema.py::test_enforced_constraints[annotation2-kwargs2-field_schema2] tests/test_schema.py::test_enforced_constraints[annotation3-kwargs3-field_schema3] tests/test_schema.py::test_enforced_constraints[annotation4-kwargs4-field_schema4] tests/test_schema.py::test_enforced_constraints[annotation5-kwargs5-field_schema5] tests/test_schema.py::test_enforced_constraints[annotation6-kwargs6-field_schema6] tests/test_schema.py::test_enforced_constraints[annotation7-kwargs7-field_schema7] tests/test_schema.py::test_real_vs_phony_constraints tests/test_schema.py::test_subfield_field_info tests/test_schema.py::test_dataclass tests/test_schema.py::test_schema_attributes tests/test_schema.py::test_model_process_schema_enum tests/test_schema.py::test_path_modify_schema tests/test_schema.py::test_frozen_set tests/test_schema.py::test_iterable tests/test_schema.py::test_new_type tests/test_schema.py::test_multiple_enums_with_same_name