diff --git a/openapi_core/schema/parameters/models.py b/openapi_core/schema/parameters/models.py
index f33773f..090bf0a 100644
--- a/openapi_core/schema/parameters/models.py
+++ b/openapi_core/schema/parameters/models.py
@@ -109,7 +109,11 @@ class Parameter(object):
             raise InvalidParameterValue(self.name, exc)
 
         try:
-            unmarshalled = self.schema.unmarshal(deserialized, custom_formatters=custom_formatters)
+            unmarshalled = self.schema.unmarshal(
+                deserialized,
+                custom_formatters=custom_formatters,
+                strict=False,
+            )
         except OpenAPISchemaError as exc:
             raise InvalidParameterValue(self.name, exc)
 
diff --git a/openapi_core/schema/schemas/factories.py b/openapi_core/schema/schemas/factories.py
index 50f04ba..136fbd0 100644
--- a/openapi_core/schema/schemas/factories.py
+++ b/openapi_core/schema/schemas/factories.py
@@ -28,7 +28,8 @@ class SchemaFactory(object):
         deprecated = schema_deref.get('deprecated', False)
         all_of_spec = schema_deref.get('allOf', None)
         one_of_spec = schema_deref.get('oneOf', None)
-        additional_properties_spec = schema_deref.get('additionalProperties')
+        additional_properties_spec = schema_deref.get('additionalProperties',
+                                                      True)
         min_items = schema_deref.get('minItems', None)
         max_items = schema_deref.get('maxItems', None)
         min_length = schema_deref.get('minLength', None)
@@ -59,8 +60,8 @@ class SchemaFactory(object):
         if items_spec:
             items = self._create_items(items_spec)
 
-        additional_properties = None
-        if additional_properties_spec:
+        additional_properties = additional_properties_spec
+        if isinstance(additional_properties_spec, dict):
             additional_properties = self.create(additional_properties_spec)
 
         return Schema(
diff --git a/openapi_core/schema/schemas/models.py b/openapi_core/schema/schemas/models.py
index f221e50..0351e1a 100644
--- a/openapi_core/schema/schemas/models.py
+++ b/openapi_core/schema/schemas/models.py
@@ -39,9 +39,6 @@ class Schema(object):
     """Represents an OpenAPI Schema."""
 
     DEFAULT_CAST_CALLABLE_GETTER = {
-        SchemaType.INTEGER: int,
-        SchemaType.NUMBER: float,
-        SchemaType.BOOLEAN: forcebool,
     }
 
     STRING_FORMAT_CALLABLE_GETTER = {
@@ -69,7 +66,7 @@ class Schema(object):
             self, schema_type=None, model=None, properties=None, items=None,
             schema_format=None, required=None, default=None, nullable=False,
             enum=None, deprecated=False, all_of=None, one_of=None,
-            additional_properties=None, min_items=None, max_items=None,
+            additional_properties=True, min_items=None, max_items=None,
             min_length=None, max_length=None, pattern=None, unique_items=False,
             minimum=None, maximum=None, multiple_of=None,
             exclusive_minimum=False, exclusive_maximum=False,
@@ -149,12 +146,15 @@ class Schema(object):
 
         return set(required)
 
-    def get_cast_mapping(self, custom_formatters=None):
+    def get_cast_mapping(self, custom_formatters=None, strict=True):
         pass_defaults = lambda f: functools.partial(
-          f, custom_formatters=custom_formatters)
+          f, custom_formatters=custom_formatters, strict=strict)
         mapping = self.DEFAULT_CAST_CALLABLE_GETTER.copy()
         mapping.update({
             SchemaType.STRING: pass_defaults(self._unmarshal_string),
+            SchemaType.BOOLEAN: pass_defaults(self._unmarshal_boolean),
+            SchemaType.INTEGER: pass_defaults(self._unmarshal_integer),
+            SchemaType.NUMBER: pass_defaults(self._unmarshal_number),
             SchemaType.ANY: pass_defaults(self._unmarshal_any),
             SchemaType.ARRAY: pass_defaults(self._unmarshal_collection),
             SchemaType.OBJECT: pass_defaults(self._unmarshal_object),
@@ -162,14 +162,15 @@ class Schema(object):
 
         return defaultdict(lambda: lambda x: x, mapping)
 
-    def cast(self, value, custom_formatters=None):
+    def cast(self, value, custom_formatters=None, strict=True):
         """Cast value to schema type"""
         if value is None:
             if not self.nullable:
                 raise InvalidSchemaValue("Null value for non-nullable schema", value, self.type)
             return self.default
 
-        cast_mapping = self.get_cast_mapping(custom_formatters=custom_formatters)
+        cast_mapping = self.get_cast_mapping(
+            custom_formatters=custom_formatters, strict=strict)
 
         if self.type is not SchemaType.STRING and value == '':
             return None
@@ -181,12 +182,12 @@ class Schema(object):
             raise InvalidSchemaValue(
                 "Failed to cast value {value} to type {type}", value, self.type)
 
-    def unmarshal(self, value, custom_formatters=None):
+    def unmarshal(self, value, custom_formatters=None, strict=True):
         """Unmarshal parameter from the value."""
         if self.deprecated:
             warnings.warn("The schema is deprecated", DeprecationWarning)
 
-        casted = self.cast(value, custom_formatters=custom_formatters)
+        casted = self.cast(value, custom_formatters=custom_formatters, strict=strict)
 
         if casted is None and not self.required:
             return None
@@ -197,7 +198,10 @@ class Schema(object):
 
         return casted
 
-    def _unmarshal_string(self, value, custom_formatters=None):
+    def _unmarshal_string(self, value, custom_formatters=None, strict=True):
+        if strict and not isinstance(value, (text_type, binary_type)):
+            raise InvalidSchemaValue("Value {value} is not of type {type}", value, self.type)
+
         try:
             schema_format = SchemaFormat(self.format)
         except ValueError:
@@ -217,7 +221,25 @@ class Schema(object):
             raise InvalidCustomFormatSchemaValue(
                 "Failed to format value {value} to format {type}: {exception}", value, self.format, exc)
 
-    def _unmarshal_any(self, value, custom_formatters=None):
+    def _unmarshal_integer(self, value, custom_formatters=None, strict=True):
+        if strict and not isinstance(value, (integer_types, )):
+            raise InvalidSchemaValue("Value {value} is not of type {type}", value, self.type)
+
+        return int(value)
+
+    def _unmarshal_number(self, value, custom_formatters=None, strict=True):
+        if strict and not isinstance(value, (float, )):
+            raise InvalidSchemaValue("Value {value} is not of type {type}", value, self.type)
+
+        return float(value)
+
+    def _unmarshal_boolean(self, value, custom_formatters=None, strict=True):
+        if strict and not isinstance(value, (bool, )):
+            raise InvalidSchemaValue("Value {value} is not of type {type}", value, self.type)
+
+        return forcebool(value)
+
+    def _unmarshal_any(self, value, custom_formatters=None, strict=True):
         types_resolve_order = [
             SchemaType.OBJECT, SchemaType.ARRAY, SchemaType.BOOLEAN,
             SchemaType.INTEGER, SchemaType.NUMBER, SchemaType.STRING,
@@ -233,16 +255,21 @@ class Schema(object):
 
         raise NoValidSchema(value)
 
-    def _unmarshal_collection(self, value, custom_formatters=None):
+    def _unmarshal_collection(self, value, custom_formatters=None, strict=True):
+        if not isinstance(value, (list, tuple)):
+            raise InvalidSchemaValue("Value {value} is not of type {type}", value, self.type)
+
         if self.items is None:
             raise UndefinedItemsSchema(self.type)
 
-        f = functools.partial(self.items.unmarshal,
-                              custom_formatters=custom_formatters)
+        f = functools.partial(
+            self.items.unmarshal,
+            custom_formatters=custom_formatters, strict=strict,
+        )
         return list(map(f, value))
 
     def _unmarshal_object(self, value, model_factory=None,
-                          custom_formatters=None):
+                          custom_formatters=None, strict=True):
         if not isinstance(value, (dict, )):
             raise InvalidSchemaValue("Value {value} is not of type {type}", value, self.type)
 
@@ -271,7 +298,7 @@ class Schema(object):
         return model_factory.create(properties, name=self.model)
 
     def _unmarshal_properties(self, value, one_of_schema=None,
-                              custom_formatters=None):
+                              custom_formatters=None, strict=True):
         all_props = self.get_all_properties()
         all_props_names = self.get_all_properties_names()
         all_req_props_names = self.get_all_required_properties_names()
@@ -285,14 +312,15 @@ class Schema(object):
 
         value_props_names = value.keys()
         extra_props = set(value_props_names) - set(all_props_names)
-        if extra_props and self.additional_properties is None:
+        if extra_props and self.additional_properties is False:
             raise UndefinedSchemaProperty(extra_props)
 
         properties = {}
-        for prop_name in extra_props:
-            prop_value = value[prop_name]
-            properties[prop_name] = self.additional_properties.unmarshal(
-                prop_value, custom_formatters=custom_formatters)
+        if self.additional_properties is not True:
+            for prop_name in extra_props:
+                prop_value = value[prop_name]
+                properties[prop_name] = self.additional_properties.unmarshal(
+                    prop_value, custom_formatters=custom_formatters)
 
         for prop_name, prop in iteritems(all_props):
             try:
@@ -516,13 +544,14 @@ class Schema(object):
 
         value_props_names = value.keys()
         extra_props = set(value_props_names) - set(all_props_names)
-        if extra_props and self.additional_properties is None:
+        if extra_props and self.additional_properties is False:
             raise UndefinedSchemaProperty(extra_props)
 
-        for prop_name in extra_props:
-            prop_value = value[prop_name]
-            self.additional_properties.validate(
-                prop_value, custom_formatters=custom_formatters)
+        if self.additional_properties is not True:
+            for prop_name in extra_props:
+                prop_value = value[prop_name]
+                self.additional_properties.validate(
+                    prop_value, custom_formatters=custom_formatters)
 
         for prop_name, prop in iteritems(all_props):
             try:
diff --git a/tests/integration/data/v3.0/petstore.yaml b/tests/integration/data/v3.0/petstore.yaml
index 3f132c3..efd817d 100644
--- a/tests/integration/data/v3.0/petstore.yaml
+++ b/tests/integration/data/v3.0/petstore.yaml
@@ -59,16 +59,7 @@ paths:
           explode: false
       responses:
         '200':
-          description: An paged array of pets
-          headers:
-            x-next:
-              description: A link to the next page of responses
-              schema:
-                type: string
-          content:
-            application/json:
-              schema:
-                $ref: "#/components/schemas/PetsData"
+          $ref: "#/components/responses/PetsResponse"
     post:
       summary: Create a pet
       operationId: createPets
@@ -295,6 +286,7 @@ components:
           $ref: "#/components/schemas/Utctime"
         name:
           type: string
+      additionalProperties: false
     TagList:
       type: array
       items:
@@ -327,9 +319,20 @@ components:
       additionalProperties:
         type: string
   responses:
-      ErrorResponse:
-        description: unexpected error
-        content:
-          application/json:
-            schema:
-              $ref: "#/components/schemas/ExtendedError"
+    ErrorResponse:
+      description: unexpected error
+      content:
+        application/json:
+          schema:
+            $ref: "#/components/schemas/ExtendedError"
+    PetsResponse:
+      description: An paged array of pets
+      headers:
+        x-next:
+          description: A link to the next page of responses
+          schema:
+            type: string
+      content:
+        application/json:
+          schema:
+            $ref: "#/components/schemas/PetsData"
diff --git a/tests/integration/test_petstore.py b/tests/integration/test_petstore.py
index e1a3c8e..b61b25d 100644
--- a/tests/integration/test_petstore.py
+++ b/tests/integration/test_petstore.py
@@ -17,8 +17,9 @@ from openapi_core.schema.parameters.models import Parameter
 from openapi_core.schema.paths.models import Path
 from openapi_core.schema.request_bodies.models import RequestBody
 from openapi_core.schema.responses.models import Response
+from openapi_core.schema.schemas.enums import SchemaType
 from openapi_core.schema.schemas.exceptions import (
-    NoValidSchema,
+    NoValidSchema, InvalidSchemaProperty, InvalidSchemaValue,
 )
 from openapi_core.schema.schemas.models import Schema
 from openapi_core.schema.servers.exceptions import InvalidServer
@@ -234,6 +235,105 @@ class TestPetstore(object):
         assert isinstance(response_result.data, BaseModel)
         assert response_result.data.data == []
 
+    def test_get_pets_response(self, spec, response_validator):
+        host_url = 'http://petstore.swagger.io/v1'
+        path_pattern = '/v1/pets'
+        query_params = {
+            'limit': '20',
+        }
+
+        request = MockRequest(
+            host_url, 'GET', '/pets',
+            path_pattern=path_pattern, args=query_params,
+        )
+
+        parameters = request.get_parameters(spec)
+        body = request.get_body(spec)
+
+        assert parameters == {
+            'query': {
+                'limit': 20,
+                'page': 1,
+                'search': '',
+            }
+        }
+        assert body is None
+
+        data_json = {
+            'data': [
+                {
+                    'id': 1,
+                    'name': 'Cat',
+                }
+            ],
+        }
+        data = json.dumps(data_json)
+        response = MockResponse(data)
+
+        response_result = response_validator.validate(request, response)
+
+        assert response_result.errors == []
+        assert isinstance(response_result.data, BaseModel)
+        assert len(response_result.data.data) == 1
+        assert response_result.data.data[0].id == 1
+        assert response_result.data.data[0].name == 'Cat'
+
+    def test_get_pets_invalid_response(self, spec, response_validator):
+        host_url = 'http://petstore.swagger.io/v1'
+        path_pattern = '/v1/pets'
+        query_params = {
+            'limit': '20',
+        }
+
+        request = MockRequest(
+            host_url, 'GET', '/pets',
+            path_pattern=path_pattern, args=query_params,
+        )
+
+        parameters = request.get_parameters(spec)
+        body = request.get_body(spec)
+
+        assert parameters == {
+            'query': {
+                'limit': 20,
+                'page': 1,
+                'search': '',
+            }
+        }
+        assert body is None
+
+        data_json = {
+            'data': [
+                {
+                    'id': 1,
+                    'name': {
+                        'first_name': 'Cat',
+                    },
+                }
+            ],
+        }
+        data = json.dumps(data_json)
+        response = MockResponse(data)
+
+        response_result = response_validator.validate(request, response)
+
+        assert response_result.errors == [
+            InvalidMediaTypeValue(
+                original_exception=InvalidSchemaProperty(
+                    property_name='data',
+                    original_exception=InvalidSchemaProperty(
+                        property_name='name',
+                        original_exception=InvalidSchemaValue(
+                            msg="Value {value} is not of type {type}",
+                            type=SchemaType.STRING,
+                            value={'first_name': 'Cat'},
+                        ),
+                    ),
+                ),
+            ),
+        ]
+        assert response_result.data is None
+
     def test_get_pets_ids_param(self, spec, response_validator):
         host_url = 'http://petstore.swagger.io/v1'
         path_pattern = '/v1/pets'
@@ -419,7 +519,7 @@ class TestPetstore(object):
         data_json = {
             'name': pet_name,
             'tag': pet_tag,
-            'position': '2',
+            'position': 2,
             'address': {
                 'street': pet_street,
                 'city': pet_city,
@@ -479,7 +579,7 @@ class TestPetstore(object):
         data_json = {
             'name': pet_name,
             'tag': pet_tag,
-            'position': '2',
+            'position': 2,
             'address': {
                 'street': pet_street,
                 'city': pet_city,
@@ -535,11 +635,11 @@ class TestPetstore(object):
         pet_tag = 'cats'
         pet_street = 'Piekna'
         pet_city = 'Warsaw'
-        pet_healthy = 'false'
+        pet_healthy = False
         data_json = {
             'name': pet_name,
             'tag': pet_tag,
-            'position': '2',
+            'position': 2,
             'address': {
                 'street': pet_street,
                 'city': pet_city,
diff --git a/tests/integration/test_validators.py b/tests/integration/test_validators.py
index bfdd4f9..c8dc2e1 100644
--- a/tests/integration/test_validators.py
+++ b/tests/integration/test_validators.py
@@ -155,7 +155,7 @@ class TestRequestValidator(object):
         data_json = {
             'name': pet_name,
             'tag': pet_tag,
-            'position': '2',
+            'position': 2,
             'address': {
                 'street': pet_street,
                 'city': pet_city,
diff --git a/tests/unit/schema/test_schemas.py b/tests/unit/schema/test_schemas.py
index a6b415d..6bedd65 100644
--- a/tests/unit/schema/test_schemas.py
+++ b/tests/unit/schema/test_schemas.py
@@ -8,6 +8,7 @@ from openapi_core.extensions.models.models import Model
 from openapi_core.schema.schemas.enums import SchemaFormat, SchemaType
 from openapi_core.schema.schemas.exceptions import (
     InvalidSchemaValue, MultipleOneOfSchema, NoOneOfSchema, OpenAPISchemaError,
+    UndefinedSchemaProperty
 )
 from openapi_core.schema.schemas.models import Schema
 
@@ -65,6 +66,13 @@ class TestSchemaUnmarshal(object):
 
         assert result == value
 
+    def test_string_float_invalid(self):
+        schema = Schema('string')
+        value = 1.23
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
     def test_string_none(self):
         schema = Schema('string')
         value = None
@@ -134,7 +142,7 @@ class TestSchemaUnmarshal(object):
         value = 'x'
 
         with mock.patch.dict(
-            Schema.STRING_FORMAT_CAST_CALLABLE_GETTER,
+            Schema.STRING_FORMAT_CALLABLE_GETTER,
             {custom_format: mock.Mock(side_effect=ValueError())},
         ), pytest.raises(
             InvalidSchemaValue, message='Failed to format value'
@@ -143,12 +151,19 @@ class TestSchemaUnmarshal(object):
 
     def test_integer_valid(self):
         schema = Schema('integer')
-        value = '123'
+        value = 123
 
         result = schema.unmarshal(value)
 
         assert result == int(value)
 
+    def test_integer_string_invalid(self):
+        schema = Schema('integer')
+        value = '123'
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
     def test_integer_enum_invalid(self):
         schema = Schema('integer', enum=[1, 2, 3])
         value = '123'
@@ -158,12 +173,19 @@ class TestSchemaUnmarshal(object):
 
     def test_integer_enum(self):
         schema = Schema('integer', enum=[1, 2, 3])
-        value = '2'
+        value = 2
 
         result = schema.unmarshal(value)
 
         assert result == int(value)
 
+    def test_integer_enum_string_invalid(self):
+        schema = Schema('integer', enum=[1, 2, 3])
+        value = '2'
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
     def test_integer_default(self):
         default_value = '123'
         schema = Schema('integer', default=default_value)
@@ -188,6 +210,65 @@ class TestSchemaUnmarshal(object):
         with pytest.raises(InvalidSchemaValue):
             schema.unmarshal(value)
 
+    def test_array_valid(self):
+        schema = Schema('array', items=Schema('integer'))
+        value = [1, 2, 3]
+
+        result = schema.unmarshal(value)
+
+        assert result == value
+
+    def test_array_of_string_string_invalid(self):
+        schema = Schema('array', items=Schema('string'))
+        value = '123'
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
+    def test_array_of_integer_string_invalid(self):
+        schema = Schema('array', items=Schema('integer'))
+        value = '123'
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
+    def test_boolean_valid(self):
+        schema = Schema('boolean')
+        value = True
+
+        result = schema.unmarshal(value)
+
+        assert result == value
+
+    def test_boolean_string_invalid(self):
+        schema = Schema('boolean')
+        value = 'True'
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
+    def test_number_valid(self):
+        schema = Schema('number')
+        value = 1.23
+
+        result = schema.unmarshal(value)
+
+        assert result == value
+
+    def test_number_string_invalid(self):
+        schema = Schema('number')
+        value = '1.23'
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
+    def test_number_int_invalid(self):
+        schema = Schema('number')
+        value = 1
+
+        with pytest.raises(InvalidSchemaValue):
+            schema.unmarshal(value)
+
 
 class TestSchemaValidate(object):
 
@@ -714,6 +795,26 @@ class TestSchemaValidate(object):
 
         assert result == value
 
+    @pytest.mark.parametrize('value', [Model({'additional': 1}), ])
+    def test_object_additional_propetries(self, value):
+        schema = Schema('object')
+
+        schema.validate(value)
+
+    @pytest.mark.parametrize('value', [Model({'additional': 1}), ])
+    def test_object_additional_propetries_false(self, value):
+        schema = Schema('object', additional_properties=False)
+
+        with pytest.raises(UndefinedSchemaProperty):
+            schema.validate(value)
+
+    @pytest.mark.parametrize('value', [Model({'additional': 1}), ])
+    def test_object_additional_propetries_object(self, value):
+        additional_properties = Schema('integer')
+        schema = Schema('object', additional_properties=additional_properties)
+
+        schema.validate(value)
+
     @pytest.mark.parametrize('value', [[], ])
     def test_list_min_items_invalid_schema(self, value):
         schema = Schema(
@@ -780,3 +881,65 @@ class TestSchemaValidate(object):
 
         with pytest.raises(Exception):
             schema.validate(value)
+
+    @pytest.mark.parametrize('value', [
+        Model({
+            'someint': 123,
+        }),
+        Model({
+            'somestr': u('content'),
+        }),
+        Model({
+            'somestr': u('content'),
+            'someint': 123,
+        }),
+    ])
+    def test_object_with_properties(self, value):
+        schema = Schema(
+            'object',
+            properties={
+                'somestr': Schema('string'),
+                'someint': Schema('integer'),
+            },
+        )
+
+        result = schema.validate(value)
+
+        assert result == value
+
+    @pytest.mark.parametrize('value', [
+        Model({
+            'somestr': Model(),
+            'someint': 123,
+        }),
+        Model({
+            'somestr': {},
+            'someint': 123,
+        }),
+        Model({
+            'somestr': [
+                'content1', 'content2'
+            ],
+            'someint': 123,
+        }),
+        Model({
+            'somestr': 123,
+            'someint': 123,
+        }),
+        Model({
+            'somestr': 'content',
+            'someint': 123,
+            'not_in_scheme_prop': 123,
+        }),
+    ])
+    def test_object_with_invalid_properties(self, value):
+        schema = Schema(
+            'object',
+            properties={
+                'somestr': Schema('string'),
+                'someint': Schema('integer'),
+            },
+        )
+
+        with pytest.raises(Exception):
+            schema.validate(value)