diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index a710df7b4..9b88784c8 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -1626,7 +1626,7 @@ class ListField(Field):
             self.fail('not_a_list', input_type=type(data).__name__)
         if not self.allow_empty and len(data) == 0:
             self.fail('empty')
-        return [self.child.run_validation(item) for item in data]
+        return self.run_child_validation(data)
 
     def to_representation(self, data):
         """
@@ -1634,6 +1634,20 @@ class ListField(Field):
         """
         return [self.child.to_representation(item) if item is not None else None for item in data]
 
+    def run_child_validation(self, data):
+        result = []
+        errors = OrderedDict()
+
+        for idx, item in enumerate(data):
+            try:
+                result.append(self.child.run_validation(item))
+            except ValidationError as e:
+                errors[idx] = e.detail
+
+        if not errors:
+            return result
+        raise ValidationError(errors)
+
 
 class DictField(Field):
     child = _UnvalidatedField()
@@ -1669,10 +1683,7 @@ class DictField(Field):
             data = html.parse_html_dict(data)
         if not isinstance(data, dict):
             self.fail('not_a_dict', input_type=type(data).__name__)
-        return {
-            six.text_type(key): self.child.run_validation(value)
-            for key, value in data.items()
-        }
+        return self.run_child_validation(data)
 
     def to_representation(self, value):
         """
@@ -1683,6 +1694,22 @@ class DictField(Field):
             for key, val in value.items()
         }
 
+    def run_child_validation(self, data):
+        result = {}
+        errors = OrderedDict()
+
+        for key, value in data.items():
+            key = six.text_type(key)
+
+            try:
+                result[key] = self.child.run_validation(value)
+            except ValidationError as e:
+                errors[key] = e.detail
+
+        if not errors:
+            return result
+        raise ValidationError(errors)
+
 
 class JSONField(Field):
     default_error_messages = {
diff --git a/tests/test_fields.py b/tests/test_fields.py
index ab26183bd..3febb3315 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -1767,7 +1767,7 @@ class TestListField(FieldValues):
     ]
     invalid_inputs = [
         ('not a list', ['Expected a list of items but got type "str".']),
-        ([1, 2, 'error'], ['A valid integer is required.']),
+        ([1, 2, 'error', 'error'], {2: ['A valid integer is required.'], 3: ['A valid integer is required.']}),
         ({'one': 'two'}, ['Expected a list of items but got type "dict".'])
     ]
     outputs = [
@@ -1840,7 +1840,7 @@ class TestDictField(FieldValues):
         ({'a': 1, 'b': '2', 3: 3}, {'a': '1', 'b': '2', '3': '3'}),
     ]
     invalid_inputs = [
-        ({'a': 1, 'b': None}, ['This field may not be null.']),
+        ({'a': 1, 'b': None, 'c': None}, {'b': ['This field may not be null.'], 'c': ['This field may not be null.']}),
         ('not a dict', ['Expected a dictionary of items but got type "str".']),
     ]
     outputs = [