diff --git a/mypy/checker.py b/mypy/checker.py
index 870c561852b6..4aa5d81d1086 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -29,6 +29,7 @@
     ARG_POS, MDEF,
     CONTRAVARIANT, COVARIANT)
 from mypy import nodes
+from mypy.typeanal import has_any_from_unimported_type
 from mypy.types import (
     Type, AnyType, CallableType, FunctionLike, Overloaded, TupleType, TypedDictType,
     Instance, NoneTyp, strip_type, TypeType,
@@ -611,7 +612,15 @@ def is_implicit_any(t: Type) -> bool:
                                 self.fail(messages.RETURN_TYPE_EXPECTED, fdef)
                             if any(is_implicit_any(t) for t in fdef.type.arg_types):
                                 self.fail(messages.ARGUMENT_TYPE_EXPECTED, fdef)
-
+                    if 'unimported' in self.options.disallow_any:
+                        if fdef.type and isinstance(fdef.type, CallableType):
+                            ret_type = fdef.type.ret_type
+                            if has_any_from_unimported_type(ret_type):
+                                self.msg.unimported_type_becomes_any("Return type", ret_type, fdef)
+                            for idx, arg_type in enumerate(fdef.type.arg_types):
+                                if has_any_from_unimported_type(arg_type):
+                                    prefix = "Argument {} to \"{}\"".format(idx + 1, fdef.name())
+                                    self.msg.unimported_type_becomes_any(prefix, arg_type, fdef)
                 if name in nodes.reverse_op_method_set:
                     self.check_reverse_op_method(item, typ, name)
                 elif name in ('__getattr__', '__getattribute__'):
@@ -1179,6 +1188,16 @@ def visit_assignment_stmt(self, s: AssignmentStmt) -> None:
         """
         self.check_assignment(s.lvalues[-1], s.rvalue, s.type is None, s.new_syntax)
 
+        if (s.type is not None and
+                'unimported' in self.options.disallow_any and
+                has_any_from_unimported_type(s.type)):
+            if isinstance(s.lvalues[-1], TupleExpr):
+                # This is a multiple assignment. Instead of figuring out which type is problematic,
+                # give a generic error message.
+                self.msg.unimported_type_becomes_any("A type on this line", AnyType(), s)
+            else:
+                self.msg.unimported_type_becomes_any("Type of variable", s.type, s)
+
         if len(s.lvalues) > 1:
             # Chained assignment (e.g. x = y = ...).
             # Make sure that rvalue type will not be reinferred.
diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
index b19a0a1bcfd2..4add26e68081 100644
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -4,6 +4,7 @@
 from typing import cast, Dict, Set, List, Tuple, Callable, Union, Optional
 
 from mypy.errors import report_internal_error
+from mypy.typeanal import has_any_from_unimported_type
 from mypy.types import (
     Type, AnyType, CallableType, Overloaded, NoneTyp, TypeVarDef,
     TupleType, TypedDictType, Instance, TypeVarType, ErasedType, UnionType,
@@ -1543,8 +1544,11 @@ def visit_cast_expr(self, expr: CastExpr) -> Type:
         """Type check a cast expression."""
         source_type = self.accept(expr.expr, type_context=AnyType(), allow_none_return=True)
         target_type = expr.type
-        if self.chk.options.warn_redundant_casts and is_same_type(source_type, target_type):
+        options = self.chk.options
+        if options.warn_redundant_casts and is_same_type(source_type, target_type):
             self.msg.redundant_cast(target_type, expr)
+        if 'unimported' in options.disallow_any and has_any_from_unimported_type(target_type):
+            self.msg.unimported_type_becomes_any("Target type of cast", target_type, expr)
         return target_type
 
     def visit_reveal_type_expr(self, expr: RevealTypeExpr) -> Type:
@@ -2229,6 +2233,11 @@ def visit_newtype_expr(self, e: NewTypeExpr) -> Type:
         return AnyType()
 
     def visit_namedtuple_expr(self, e: NamedTupleExpr) -> Type:
+        tuple_type = e.info.tuple_type
+        if tuple_type:
+            if ('unimported' in self.chk.options.disallow_any and
+                    has_any_from_unimported_type(tuple_type)):
+                self.msg.unimported_type_becomes_any("NamedTuple type", tuple_type, e)
         # TODO: Perhaps return a type object type?
         return AnyType()
 
diff --git a/mypy/main.py b/mypy/main.py
index a5511671c966..5229071773ba 100644
--- a/mypy/main.py
+++ b/mypy/main.py
@@ -179,6 +179,7 @@ def process_options(args: List[str],
 
     strict_flag_names = []  # type: List[str]
     strict_flag_assignments = []  # type: List[Tuple[str, bool]]
+    disallow_any_options = ['unimported']
 
     def add_invertible_flag(flag: str,
                             *,
@@ -203,6 +204,17 @@ def add_invertible_flag(flag: str,
             strict_flag_names.append(flag)
             strict_flag_assignments.append((dest, not default))
 
+    def disallow_any_argument_type(raw_options: str) -> List[str]:
+        flag_options = raw_options.split(',')
+        for option in flag_options:
+            if option not in disallow_any_options:
+                formatted_valid_options = ', '.join(
+                    "'{}'".format(o) for o in disallow_any_options)
+                message = "Invalid '--disallow-any' option '{}' (valid options are: {}).".format(
+                    option, formatted_valid_options)
+                raise argparse.ArgumentError(None, message)
+        return flag_options
+
     # Unless otherwise specified, arguments will be parsed directly onto an
     # Options object.  Options that require further processing should have
     # their `dest` prefixed with `special-opts:`, which will cause them to be
@@ -222,6 +234,10 @@ def add_invertible_flag(flag: str,
                         help="silently ignore imports of missing modules")
     parser.add_argument('--follow-imports', choices=['normal', 'silent', 'skip', 'error'],
                         default='normal', help="how to treat imports (default normal)")
+    parser.add_argument('--disallow-any', type=disallow_any_argument_type, default=[],
+                        metavar='{{{}}}'.format(', '.join(disallow_any_options)),
+                        help="disallow various types of Any in a module. Takes a comma-separated "
+                             "list of options (defaults to all options disabled)")
     add_invertible_flag('--disallow-untyped-calls', default=False, strict_flag=True,
                         help="disallow calling functions without type annotations"
                         " from functions with type annotations")
diff --git a/mypy/messages.py b/mypy/messages.py
index 5c2f5d16fdc7..c63b44905d51 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -855,6 +855,10 @@ def unsupported_type_type(self, item: Type, context: Context) -> None:
     def redundant_cast(self, typ: Type, context: Context) -> None:
         self.note('Redundant cast to {}'.format(self.format(typ)), context)
 
+    def unimported_type_becomes_any(self, prefix: str, typ: Type, ctx: Context) -> None:
+        self.fail("{} becomes {} due to an unfollowed import".format(prefix, self.format(typ)),
+                  ctx)
+
     def typeddict_instantiated_with_unexpected_items(self,
                                                      expected_item_names: List[str],
                                                      actual_item_names: List[str],
diff --git a/mypy/options.py b/mypy/options.py
index 8c8764200800..b558470520f3 100644
--- a/mypy/options.py
+++ b/mypy/options.py
@@ -2,7 +2,7 @@
 import pprint
 import sys
 
-from typing import Any, Mapping, Optional, Tuple, List, Pattern, Dict
+from typing import Mapping, Optional, Tuple, List, Pattern, Dict
 
 from mypy import defaults
 
@@ -19,6 +19,7 @@ class Options:
     PER_MODULE_OPTIONS = {
         "ignore_missing_imports",
         "follow_imports",
+        "disallow_any",
         "disallow_untyped_calls",
         "disallow_untyped_defs",
         "check_untyped_defs",
@@ -44,6 +45,7 @@ def __init__(self) -> None:
         self.report_dirs = {}  # type: Dict[str, str]
         self.ignore_missing_imports = False
         self.follow_imports = 'normal'  # normal|silent|skip|error
+        self.disallow_any = []  # type: List[str]
 
         # Disallow calling untyped functions from typed ones
         self.disallow_untyped_calls = False
diff --git a/mypy/semanal.py b/mypy/semanal.py
index b14e3dd9076e..8272efeb6152 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -75,7 +75,7 @@
 from mypy.visitor import NodeVisitor
 from mypy.traverser import TraverserVisitor
 from mypy.errors import Errors, report_internal_error
-from mypy.messages import CANNOT_ASSIGN_TO_TYPE
+from mypy.messages import CANNOT_ASSIGN_TO_TYPE, MessageBuilder
 from mypy.types import (
     NoneTyp, CallableType, Overloaded, Instance, Type, TypeVarType, AnyType,
     FunctionLike, UnboundType, TypeList, TypeVarDef, TypeType,
@@ -85,7 +85,7 @@
 from mypy.nodes import implicit_module_attrs
 from mypy.typeanal import (
     TypeAnalyser, TypeAnalyserPass3, analyze_type_alias, no_subscript_builtin_alias,
-    TypeVariableQuery, TypeVarList, remove_dups,
+    TypeVariableQuery, TypeVarList, remove_dups, has_any_from_unimported_type
 )
 from mypy.exprtotype import expr_to_unanalyzed_type, TypeTranslationError
 from mypy.sametypes import is_same_type
@@ -236,6 +236,7 @@ def __init__(self,
         self.lib_path = lib_path
         self.errors = errors
         self.modules = modules
+        self.msg = MessageBuilder(errors, modules)
         self.missing_modules = missing_modules
         self.postpone_nested_functions_stack = [FUNCTION_BOTH_PHASES]
         self.postponed_functions_stack = []
@@ -974,6 +975,12 @@ def analyze_base_classes(self, defn: ClassDef) -> None:
             else:
                 self.fail('Invalid base class', base_expr)
                 info.fallback_to_any = True
+            if 'unimported' in self.options.disallow_any and has_any_from_unimported_type(base):
+                if isinstance(base_expr, (NameExpr, MemberExpr)):
+                    prefix = "Base type {}".format(base_expr.name)
+                else:
+                    prefix = "Base type"
+                self.msg.unimported_type_becomes_any(prefix, base, base_expr)
 
         # Add 'object' as implicit base if there is no other base class.
         if (not base_types and defn.fullname != 'builtins.object'):
@@ -1428,7 +1435,7 @@ def add_unknown_symbol(self, name: str, context: Context, is_import: bool = Fals
         else:
             var._fullname = self.qualified_name(name)
         var.is_ready = True
-        var.type = AnyType()
+        var.type = AnyType(from_unimported_type=is_import)
         var.is_suppressed_import = is_import
         self.add_symbol(name, SymbolTableNode(GDEF, var, self.cur_mod_id), context)
 
@@ -1875,6 +1882,16 @@ def process_typevar_declaration(self, s: AssignmentStmt) -> None:
             return
         variance, upper_bound = res
 
+        if 'unimported' in self.options.disallow_any:
+            for idx, constraint in enumerate(values, start=1):
+                if has_any_from_unimported_type(constraint):
+                    prefix = "Constraint {}".format(idx)
+                    self.msg.unimported_type_becomes_any(prefix, constraint, s)
+
+            if has_any_from_unimported_type(upper_bound):
+                prefix = "Upper bound of type variable"
+                self.msg.unimported_type_becomes_any(prefix, upper_bound, s)
+
         # Yes, it's a valid type variable definition! Add it to the symbol table.
         node = self.lookup(name, s)
         node.kind = TVAR
diff --git a/mypy/typeanal.py b/mypy/typeanal.py
index 2a506b7a5378..f9ff0ab66fe3 100644
--- a/mypy/typeanal.py
+++ b/mypy/typeanal.py
@@ -232,7 +232,7 @@ def visit_unbound_type(self, t: UnboundType) -> Type:
                     # context. This is slightly problematic as it allows using the type 'Any'
                     # as a base class -- however, this will fail soon at runtime so the problem
                     # is pretty minor.
-                    return AnyType()
+                    return AnyType(from_unimported_type=True)
                 # Allow unbound type variables when defining an alias
                 if not (self.aliasing and sym.kind == TVAR and
                         self.tvar_scope.get_binding(sym) is None):
@@ -731,6 +731,23 @@ def visit_callable_type(self, t: CallableType) -> TypeVarList:
             return []
 
 
+def has_any_from_unimported_type(t: Type) -> bool:
+    """Return true if this type is Any because an import was not followed.
+
+    If type t is such Any type or has type arguments that contain such Any type
+    this function will return true.
+    """
+    return t.accept(HasAnyFromUnimportedType())
+
+
+class HasAnyFromUnimportedType(TypeQuery[bool]):
+    def __init__(self) -> None:
+        super().__init__(any)
+
+    def visit_any(self, t: AnyType) -> bool:
+        return t.from_unimported_type
+
+
 def make_optional_type(t: Type) -> Type:
     """Return the type corresponding to Optional[t].
 
diff --git a/mypy/types.py b/mypy/types.py
index c17bb063f5fb..0cf44d724bb7 100644
--- a/mypy/types.py
+++ b/mypy/types.py
@@ -272,9 +272,16 @@ def serialize(self) -> JsonDict:
 class AnyType(Type):
     """The type 'Any'."""
 
-    def __init__(self, implicit: bool = False, line: int = -1, column: int = -1) -> None:
+    def __init__(self,
+                 implicit: bool = False,
+                 from_unimported_type: bool = False,
+                 line: int = -1,
+                 column: int = -1) -> None:
         super().__init__(line, column)
+        # Was this Any type was inferred without a type annotation?
         self.implicit = implicit
+        # Does this come from an unfollowed import? See --disallow-any=unimported option
+        self.from_unimported_type = from_unimported_type
 
     def accept(self, visitor: 'TypeVisitor[T]') -> T:
         return visitor.visit_any(self)
diff --git a/test-data/unit/check-flags.test b/test-data/unit/check-flags.test
index 2b0e5549589a..6f8dcdd4a94b 100644
--- a/test-data/unit/check-flags.test
+++ b/test-data/unit/check-flags.test
@@ -376,3 +376,136 @@ if y:  # E: Condition must be a boolean
 if z:  # E: Condition must be a boolean
   pass
 [builtins fixtures/bool.pyi]
+
+[case testDisallowImplicitTypesIgnoreMissingTypes]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import MyType
+
+def f(x: MyType) -> None:  # E: Argument 1 to "f" becomes "Any" due to an unfollowed import
+    pass
+
+[case testDisallowImplicitTypes]
+# flags: --disallow-any=unimported
+from missing import MyType
+
+def f(x: MyType) -> None:
+    pass
+[out]
+main:2: error: Cannot find module named 'missing'
+main:2: note: (Perhaps setting MYPYPATH or using the "--ignore-missing-imports" flag would help)
+main:4: error: Argument 1 to "f" becomes "Any" due to an unfollowed import
+
+[case testDisallowImplicitAnyVariableDefinition]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import Unchecked
+
+t: Unchecked = 12  # E: Type of variable becomes "Any" due to an unfollowed import
+
+[case testDisallowImplicitAnyGeneric]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import Unchecked
+from typing import List
+
+def foo(l: List[Unchecked]) -> List[Unchecked]:
+    t = []  # type: List[Unchecked]
+    return l
+[builtins fixtures/list.pyi]
+[out]
+main:5: error: Return type becomes List[Any] due to an unfollowed import
+main:5: error: Argument 1 to "foo" becomes List[Any] due to an unfollowed import
+main:6: error: Type of variable becomes List[Any] due to an unfollowed import
+
+[case testDisallowImplicitAnyInherit]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import Unchecked
+from typing import List
+
+class C(Unchecked): # E: Base type Unchecked becomes "Any" due to an unfollowed import
+    pass
+
+class A(List[Unchecked]): # E: Base type becomes List[Any] due to an unfollowed import
+    pass
+[builtins fixtures/list.pyi]
+
+[case testDisallowImplicitAnyAlias]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import Unchecked
+from typing import List
+
+X = List[Unchecked]
+
+def f(x: X) -> None:  # E: Argument 1 to "f" becomes List[Any] due to an unfollowed import
+    pass
+[builtins fixtures/list.pyi]
+
+[case testDisallowImplicitAnyCast]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import Unchecked
+from typing import List, cast
+
+
+foo = [1, 2, 3]
+cast(List[Unchecked], foo)  # E: Target type of cast becomes List[Any] due to an unfollowed import
+cast(Unchecked, foo)  # E: Target type of cast becomes "Any" due to an unfollowed import
+[builtins fixtures/list.pyi]
+
+[case testDisallowImplicitAnyNamedTuple]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from typing import List, NamedTuple
+from missing import Unchecked
+
+Point = NamedTuple('Point', [('x', List[Unchecked]),
+                             ('y', Unchecked)])
+[builtins fixtures/list.pyi]
+[out]
+main:5: error: NamedTuple type becomes "Tuple[List[Any], Any]" due to an unfollowed import
+
+[case testDisallowImplicitAnyTypeVarConstraints]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from typing import List, NamedTuple, TypeVar, Any
+from missing import Unchecked
+
+T = TypeVar('T', Unchecked, List[Unchecked], str)
+[builtins fixtures/list.pyi]
+[out]
+main:5: error: Constraint 1 becomes "Any" due to an unfollowed import
+main:5: error: Constraint 2 becomes List[Any] due to an unfollowed import
+
+[case testDisallowImplicitAnyNewType]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from typing import NewType
+from missing import Unchecked
+
+Baz = NewType('Baz', Unchecked)
+[out]
+main:5: error: Argument 2 to NewType(...) must be subclassable (got Any)
+
+[case testDisallowImplicitAnyCallableAndTuple]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from typing import Callable, Tuple
+from missing import Unchecked
+
+def foo(f: Callable[[], Unchecked]) -> Tuple[Unchecked]:
+    return f()
+[builtins fixtures/list.pyi]
+[out]
+main:5: error: Return type becomes "Tuple[Any]" due to an unfollowed import
+main:5: error: Argument 1 to "foo" becomes Callable[[], Any] due to an unfollowed import
+
+[case testDisallowImplicitAnySubclassingExplicitAny]
+# flags: --ignore-missing-imports --disallow-any=unimported --disallow-subclassing-any
+from typing import Any
+
+class C(Any): # E: Class cannot subclass 'Any' (has type 'Any')
+    pass
+
+[case testDisallowImplicitAnyVarDeclaration]
+# flags: --ignore-missing-imports --disallow-any=unimported
+from missing import Unchecked
+
+foo: Unchecked = ""
+foo = ""
+x, y = 1, 2  # type: Unchecked, Unchecked
+[out]
+main:4: error: Type of variable becomes "Any" due to an unfollowed import
+main:6: error: A type on this line becomes "Any" due to an unfollowed import