diff --git a/mypy/checker.py b/mypy/checker.py
index e25368a19d0c..ccbab33b7b96 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -36,7 +36,7 @@
     is_optional, remove_optional
 )
 from mypy.sametypes import is_same_type
-from mypy.messages import MessageBuilder, make_inferred_type_note
+from mypy.messages import MessageBuilder, make_inferred_type_note, append_invariance_notes
 import mypy.checkexpr
 from mypy.checkmember import (
     map_type_from_supertype, bind_self, erase_to_bound, type_object_type,
@@ -3569,6 +3569,7 @@ def check_subtype(self, subtype: Type, supertype: Type, context: Context,
                 return False
             extra_info = []  # type: List[str]
             note_msg = ''
+            notes = []  # type: List[str]
             if subtype_label is not None or supertype_label is not None:
                 subtype_str, supertype_str = self.msg.format_distinctly(subtype, supertype)
                 if subtype_label is not None:
@@ -3577,9 +3578,13 @@ def check_subtype(self, subtype: Type, supertype: Type, context: Context,
                     extra_info.append(supertype_label + ' ' + supertype_str)
                 note_msg = make_inferred_type_note(context, subtype,
                                                    supertype, supertype_str)
+                if isinstance(subtype, Instance) and isinstance(supertype, Instance):
+                    notes = append_invariance_notes([], subtype, supertype)
             if extra_info:
                 msg += ' (' + ', '.join(extra_info) + ')'
             self.fail(msg, context)
+            for note in notes:
+                self.msg.note(note, context)
             if note_msg:
                 self.note(note_msg, context)
             if (isinstance(supertype, Instance) and supertype.type.is_protocol and
diff --git a/test-data/unit/check-basic.test b/test-data/unit/check-basic.test
index 629d6bf291d2..53797ada44e8 100644
--- a/test-data/unit/check-basic.test
+++ b/test-data/unit/check-basic.test
@@ -372,3 +372,21 @@ none = None
 b = none.__bool__()
 reveal_type(b)  # E: Revealed type is 'builtins.bool'
 [builtins fixtures/bool.pyi]
+
+[case testAssignmentInvariantNoteForList]
+from typing import List
+x: List[int]
+y: List[float]
+y = x # E: Incompatible types in assignment (expression has type "List[int]", variable has type "List[float]") \
+     # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+     # N: Consider using "Sequence" instead, which is covariant
+[builtins fixtures/list.pyi]
+
+[case testAssignmentInvariantNoteForDict]
+from typing import Dict
+x: Dict[str, int]
+y: Dict[str, float]
+y = x # E: Incompatible types in assignment (expression has type "Dict[str, int]", variable has type "Dict[str, float]") \
+     # N: "Dict" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+     # N: Consider using "Mapping" instead, which is covariant in the value type
+[builtins fixtures/dict.pyi]
diff --git a/test-data/unit/check-functions.test b/test-data/unit/check-functions.test
index 0114e3d10eab..9bcc09e28d8d 100644
--- a/test-data/unit/check-functions.test
+++ b/test-data/unit/check-functions.test
@@ -2364,12 +2364,16 @@ from typing import Union, Dict, List
 def f() -> List[Union[str, int]]:
     x = ['a']
     return x # E: Incompatible return value type (got "List[str]", expected "List[Union[str, int]]") \
-# N: Perhaps you need a type annotation for "x"? Suggestion: "List[Union[str, int]]"
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant \
+      # N: Perhaps you need a type annotation for "x"? Suggestion: "List[Union[str, int]]"
 
 def g() -> Dict[str, Union[str, int]]:
     x = {'a': 'a'}
     return x # E: Incompatible return value type (got "Dict[str, str]", expected "Dict[str, Union[str, int]]") \
-# N: Perhaps you need a type annotation for "x"? Suggestion: "Dict[str, Union[str, int]]"
+      # N: "Dict" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Mapping" instead, which is covariant in the value type \
+      # N: Perhaps you need a type annotation for "x"? Suggestion: "Dict[str, Union[str, int]]"
 
 def h() -> Dict[Union[str, int], str]:
     x = {'a': 'a'}
@@ -2378,7 +2382,9 @@ def h() -> Dict[Union[str, int], str]:
 
 def i() -> List[Union[int, float]]:
     x: List[int] = [1]
-    return x # E: Incompatible return value type (got "List[int]", expected "List[Union[int, float]]")
+    return x # E: Incompatible return value type (got "List[int]", expected "List[Union[int, float]]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant
 
 [builtins fixtures/dict.pyi]
 
diff --git a/test-data/unit/check-inference-context.test b/test-data/unit/check-inference-context.test
index af3abab0ce23..58d561ffafb7 100644
--- a/test-data/unit/check-inference-context.test
+++ b/test-data/unit/check-inference-context.test
@@ -1320,7 +1320,10 @@ T = TypeVar('T', bound=int)
 def f(x: List[T]) -> List[T]: ...
 
 # TODO: improve error message for such cases, see #3283 and #5706
-y: List[str] = f([])  # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[str]")
+y: List[str] = f([]) \
+ # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[str]") \
+ # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+ # N: Consider using "Sequence" instead, which is covariant
 [builtins fixtures/list.pyi]
 
 [case testWideOuterContextNoArgs]
@@ -1339,7 +1342,10 @@ from typing import TypeVar, Optional, List
 T = TypeVar('T', bound=int)
 def f(x: Optional[T] = None) -> List[T]: ...
 
-y: List[str] = f()  # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[str]")
+y: List[str] = f()  \
+      # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[str]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant
 [builtins fixtures/list.pyi]
 
 [case testUseCovariantGenericOuterContext]
diff --git a/test-data/unit/check-inference.test b/test-data/unit/check-inference.test
index 656c1b67f5ad..9d7887d05ae9 100644
--- a/test-data/unit/check-inference.test
+++ b/test-data/unit/check-inference.test
@@ -1331,7 +1331,10 @@ if int():
 if int():
     a = x2
 if int():
-    a = x3 # E: Incompatible types in assignment (expression has type "List[B]", variable has type "List[A]")
+    a = x3 \
+     # E: Incompatible types in assignment (expression has type "List[B]", variable has type "List[A]") \
+     # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+     # N: Consider using "Sequence" instead, which is covariant
 [builtins fixtures/list.pyi]
 [typing fixtures/typing-full.pyi]
 
@@ -1351,7 +1354,10 @@ if int():
 if int():
     a = x2
 if int():
-    a = x3 # E: Incompatible types in assignment (expression has type "List[B]", variable has type "List[A]")
+    a = x3 \
+     # E: Incompatible types in assignment (expression has type "List[B]", variable has type "List[A]") \
+     # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+     # N: Consider using "Sequence" instead, which is covariant
 [builtins fixtures/list.pyi]
 [typing fixtures/typing-full.pyi]
 
diff --git a/test-data/unit/check-typevar-values.test b/test-data/unit/check-typevar-values.test
index 9e9056845dfc..69a54dc34bd9 100644
--- a/test-data/unit/check-typevar-values.test
+++ b/test-data/unit/check-typevar-values.test
@@ -19,7 +19,10 @@ o = [object()]
 if int():
     i = f(1)
     s = f('')
-    o = f(1) # E: Incompatible types in assignment (expression has type "List[int]", variable has type "List[object]")
+    o = f(1) \
+      # E: Incompatible types in assignment (expression has type "List[int]", variable has type "List[object]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant
 [builtins fixtures/list.pyi]
 
 [case testCallGenericFunctionWithTypeVarValueRestrictionAndAnyArgs]
diff --git a/test-data/unit/check-varargs.test b/test-data/unit/check-varargs.test
index 357b0ed63a62..cad333eb2746 100644
--- a/test-data/unit/check-varargs.test
+++ b/test-data/unit/check-varargs.test
@@ -586,18 +586,29 @@ ab = None # type: List[B]
 if int():
     a, aa = G().f(*[a]) \
       # E: Incompatible types in assignment (expression has type "List[A]", variable has type "A") \
-      # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[A]")
+      # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[A]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant
+
 if int():
     aa, a = G().f(*[a]) # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "A")
 if int():
     ab, aa = G().f(*[a]) \
       # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[A]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant \
       # E: Argument 1 to "f" of "G" has incompatible type "*List[A]"; expected "B"
 
 if int():
-    ao, ao = G().f(*[a]) # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[object]")
+    ao, ao = G().f(*[a]) \
+      # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[object]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant
 if int():
-    aa, aa = G().f(*[a]) # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[A]")
+    aa, aa = G().f(*[a]) \
+      # E: Incompatible types in assignment (expression has type "List[<nothing>]", variable has type "List[A]") \
+      # N: "List" is invariant -- see http://mypy.readthedocs.io/en/latest/common_issues.html#variance \
+      # N: Consider using "Sequence" instead, which is covariant
 
 class G(Generic[T]):
     def f(self, *a: S) -> Tuple[List[S], List[T]]: