diff --git a/mypy/checker.py b/mypy/checker.py
index 307afe8568d5..efadddb2a491 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -3,6 +3,7 @@
 import itertools
 import fnmatch
 from contextlib import contextmanager
+import sys
 
 from typing import (
     Dict, Set, List, cast, Tuple, TypeVar, Union, Optional, NamedTuple, Iterator
@@ -311,12 +312,19 @@ def check_overlapping_overloads(self, defn: OverloadedFuncDef) -> None:
     # for functions decorated with `@types.coroutine` or
     # `@asyncio.coroutine`.  Its single parameter corresponds to tr.
     #
+    # PEP 525 adds a new type, the asynchronous generator, which was
+    # first released in Python 3.6. Async generators are `async def`
+    # functions that can also `yield` values. They can be parameterized
+    # with two types, ty and tc, because they cannot return a value.
+    #
     # There are several useful methods, each taking a type t and a
     # flag c indicating whether it's for a generator or coroutine:
     #
     # - is_generator_return_type(t, c) returns whether t is a Generator,
     #   Iterator, Iterable (if not c), or Awaitable (if c), or
     #   AwaitableGenerator (regardless of c).
+    # - is_async_generator_return_type(t) returns whether t is an
+    #   AsyncGenerator.
     # - get_generator_yield_type(t, c) returns ty.
     # - get_generator_receive_type(t, c) returns tc.
     # - get_generator_return_type(t, c) returns tr.
@@ -338,11 +346,24 @@ def is_generator_return_type(self, typ: Type, is_coroutine: bool) -> bool:
                 return True
         return isinstance(typ, Instance) and typ.type.fullname() == 'typing.AwaitableGenerator'
 
+    def is_async_generator_return_type(self, typ: Type) -> bool:
+        """Is `typ` a valid type for an async generator?
+
+        True if `typ` is a supertype of AsyncGenerator.
+        """
+        try:
+            agt = self.named_generic_type('typing.AsyncGenerator', [AnyType(), AnyType()])
+        except KeyError:
+            # we're running on a version of typing that doesn't have AsyncGenerator yet
+            return False
+        return is_subtype(agt, typ)
+
     def get_generator_yield_type(self, return_type: Type, is_coroutine: bool) -> Type:
         """Given the declared return type of a generator (t), return the type it yields (ty)."""
         if isinstance(return_type, AnyType):
             return AnyType()
-        elif not self.is_generator_return_type(return_type, is_coroutine):
+        elif (not self.is_generator_return_type(return_type, is_coroutine)
+                and not self.is_async_generator_return_type(return_type)):
             # If the function doesn't have a proper Generator (or
             # Awaitable) return type, anything is permissible.
             return AnyType()
@@ -353,7 +374,7 @@ def get_generator_yield_type(self, return_type: Type, is_coroutine: bool) -> Typ
             # Awaitable: ty is Any.
             return AnyType()
         elif return_type.args:
-            # AwaitableGenerator, Generator, Iterator, or Iterable; ty is args[0].
+            # AwaitableGenerator, Generator, AsyncGenerator, Iterator, or Iterable; ty is args[0].
             ret_type = return_type.args[0]
             # TODO not best fix, better have dedicated yield token
             if isinstance(ret_type, NoneTyp):
@@ -373,7 +394,8 @@ def get_generator_receive_type(self, return_type: Type, is_coroutine: bool) -> T
         """Given a declared generator return type (t), return the type its yield receives (tc)."""
         if isinstance(return_type, AnyType):
             return AnyType()
-        elif not self.is_generator_return_type(return_type, is_coroutine):
+        elif (not self.is_generator_return_type(return_type, is_coroutine)
+                and not self.is_async_generator_return_type(return_type)):
             # If the function doesn't have a proper Generator (or
             # Awaitable) return type, anything is permissible.
             return AnyType()
@@ -387,6 +409,8 @@ def get_generator_receive_type(self, return_type: Type, is_coroutine: bool) -> T
               and len(return_type.args) >= 3):
             # Generator: tc is args[1].
             return return_type.args[1]
+        elif return_type.type.fullname() == 'typing.AsyncGenerator' and len(return_type.args) >= 2:
+            return return_type.args[1]
         else:
             # `return_type` is a supertype of Generator, so callers won't be able to send it
             # values.  IOW, tc is None.
@@ -537,8 +561,12 @@ def is_implicit_any(t: Type) -> bool:
 
                 # Check that Generator functions have the appropriate return type.
                 if defn.is_generator:
-                    if not self.is_generator_return_type(typ.ret_type, defn.is_coroutine):
-                        self.fail(messages.INVALID_RETURN_TYPE_FOR_GENERATOR, typ)
+                    if defn.is_async_generator:
+                        if not self.is_async_generator_return_type(typ.ret_type):
+                            self.fail(messages.INVALID_RETURN_TYPE_FOR_ASYNC_GENERATOR, typ)
+                    else:
+                        if not self.is_generator_return_type(typ.ret_type, defn.is_coroutine):
+                            self.fail(messages.INVALID_RETURN_TYPE_FOR_GENERATOR, typ)
 
                     # Python 2 generators aren't allowed to return values.
                     if (self.options.python_version[0] == 2 and
@@ -1743,6 +1771,11 @@ def check_return_stmt(self, s: ReturnStmt) -> None:
             if s.expr:
                 # Return with a value.
                 typ = self.expr_checker.accept(s.expr, return_type)
+
+                if defn.is_async_generator:
+                    self.fail("'return' with value in async generator is not allowed", s)
+                    return
+
                 # Returning a value of type Any is always fine.
                 if isinstance(typ, AnyType):
                     # (Unless you asked to be warned in that case, and the
diff --git a/mypy/messages.py b/mypy/messages.py
index 782df03f5bd6..88edba48a38c 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -34,6 +34,9 @@
 INVALID_EXCEPTION_TYPE = 'Exception type must be derived from BaseException'
 INVALID_RETURN_TYPE_FOR_GENERATOR = \
     'The return type of a generator function should be "Generator" or one of its supertypes'
+INVALID_RETURN_TYPE_FOR_ASYNC_GENERATOR = \
+    'The return type of an async generator function should be "AsyncGenerator" or one of its ' \
+    'supertypes'
 INVALID_GENERATOR_RETURN_ITEM_TYPE = \
     'The return type of a generator function must be None in its third type parameter in Python 2'
 YIELD_VALUE_EXPECTED = 'Yield value expected'
diff --git a/mypy/nodes.py b/mypy/nodes.py
index 1346581ef8d3..f9599c13cf4b 100644
--- a/mypy/nodes.py
+++ b/mypy/nodes.py
@@ -481,6 +481,7 @@ class FuncItem(FuncBase):
     is_overload = False
     is_generator = False   # Contains a yield statement?
     is_coroutine = False   # Defined using 'async def' syntax?
+    is_async_generator = False  # Is an async def generator?
     is_awaitable_coroutine = False  # Decorated with '@{typing,asyncio}.coroutine'?
     is_static = False      # Uses @staticmethod?
     is_class = False       # Uses @classmethod?
@@ -488,8 +489,8 @@ class FuncItem(FuncBase):
     expanded = None  # type: List[FuncItem]
 
     FLAGS = [
-        'is_overload', 'is_generator', 'is_coroutine', 'is_awaitable_coroutine',
-        'is_static', 'is_class',
+        'is_overload', 'is_generator', 'is_coroutine', 'is_async_generator',
+        'is_awaitable_coroutine', 'is_static', 'is_class',
     ]
 
     def __init__(self, arguments: List[Argument], body: 'Block',
diff --git a/mypy/semanal.py b/mypy/semanal.py
index 0236bddf5270..e11b89574aaa 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -324,11 +324,15 @@ def visit_func_def(self, defn: FuncDef) -> None:
             self.errors.push_function(defn.name())
             self.analyze_function(defn)
             if defn.is_coroutine and isinstance(defn.type, CallableType):
-                # A coroutine defined as `async def foo(...) -> T: ...`
-                # has external return type `Awaitable[T]`.
-                defn.type = defn.type.copy_modified(
-                    ret_type = self.named_type_or_none('typing.Awaitable',
-                                                       [defn.type.ret_type]))
+                if defn.is_async_generator:
+                    # Async generator types are handled elsewhere
+                    pass
+                else:
+                    # A coroutine defined as `async def foo(...) -> T: ...`
+                    # has external return type `Awaitable[T]`.
+                    defn.type = defn.type.copy_modified(
+                        ret_type = self.named_type_or_none('typing.Awaitable',
+                                                           [defn.type.ret_type]))
             self.errors.pop_function()
 
     def prepare_method_signature(self, func: FuncDef) -> None:
@@ -2842,7 +2846,11 @@ def visit_yield_expr(self, expr: YieldExpr) -> None:
             self.fail("'yield' outside function", expr, True, blocker=True)
         else:
             if self.function_stack[-1].is_coroutine:
-                self.fail("'yield' in async function", expr, True, blocker=True)
+                if self.options.python_version < (3, 6):
+                    self.fail("'yield' in async function", expr, True, blocker=True)
+                else:
+                    self.function_stack[-1].is_generator = True
+                    self.function_stack[-1].is_async_generator = True
             else:
                 self.function_stack[-1].is_generator = True
         if expr.expr:
diff --git a/test-data/unit/check-async-await.test b/test-data/unit/check-async-await.test
index ac2ada81d7d7..ebae58ee6b1d 100644
--- a/test-data/unit/check-async-await.test
+++ b/test-data/unit/check-async-await.test
@@ -326,18 +326,15 @@ async def f() -> None:
 [builtins fixtures/async_await.pyi]
 
 [case testNoYieldInAsyncDef]
+# flags: --python-version 3.5
 
 async def f():
-    yield None
+    yield None  # E: 'yield' in async function
 async def g():
-    yield
+    yield  # E: 'yield' in async function
 async def h():
-    x = yield
+    x = yield  # E: 'yield' in async function
 [builtins fixtures/async_await.pyi]
-[out]
-main:3: error: 'yield' in async function
-main:5: error: 'yield' in async function
-main:7: error: 'yield' in async function
 
 [case testNoYieldFromInAsyncDef]
 
@@ -410,6 +407,156 @@ def f() -> Generator[int, str, int]:
 [builtins fixtures/async_await.pyi]
 [out]
 
+-- Async generators (PEP 525), some test cases adapted from the PEP text
+-- ---------------------------------------------------------------------
+
+[case testAsyncGenerator]
+# flags: --python-version 3.6
+from typing import AsyncGenerator, Generator
+
+async def f() -> int:
+    return 42
+
+async def g() -> AsyncGenerator[int, None]:
+    value = await f()
+    reveal_type(value)  # E: Revealed type is 'builtins.int*'
+    yield value
+
+    yield 'not an int'  # E: Incompatible types in yield (actual type "str", expected type "int")
+    # return without a value is fine
+    return
+reveal_type(g)  # E: Revealed type is 'def () -> typing.AsyncGenerator[builtins.int, void]'
+reveal_type(g())  # E: Revealed type is 'typing.AsyncGenerator[builtins.int, void]'
+
+async def h() -> None:
+    async for item in g():
+        reveal_type(item)  # E: Revealed type is 'builtins.int*'
+
+async def wrong_return() -> Generator[int, None, None]:  # E: The return type of an async generator function should be "AsyncGenerator" or one of its supertypes
+    yield 3
+
+[builtins fixtures/dict.pyi]
+
+[case testAsyncGeneratorReturnIterator]
+# flags: --python-version 3.6
+from typing import AsyncIterator
+
+async def gen() -> AsyncIterator[int]:
+    yield 3
+
+    yield 'not an int'  # E: Incompatible types in yield (actual type "str", expected type "int")
+
+async def use_gen() -> None:
+    async for item in gen():
+        reveal_type(item)  # E: Revealed type is 'builtins.int*'
+
+[builtins fixtures/dict.pyi]
+
+[case testAsyncGeneratorManualIter]
+# flags: --python-version 3.6
+from typing import AsyncGenerator
+
+async def genfunc() -> AsyncGenerator[int, None]:
+    yield 1
+    yield 2
+
+async def user() -> None:
+    gen = genfunc()
+
+    reveal_type(gen.__aiter__())  # E: Revealed type is 'typing.AsyncGenerator[builtins.int*, void]'
+
+    reveal_type(await gen.__anext__())  # E: Revealed type is 'builtins.int*'
+
+[builtins fixtures/dict.pyi]
+
+[case testAsyncGeneratorAsend]
+# flags: --fast-parser --python-version 3.6
+from typing import AsyncGenerator
+
+async def f() -> None:
+    pass
+
+async def gen() -> AsyncGenerator[int, str]:
+    await f()
+    v = yield 42
+    reveal_type(v)  # E: Revealed type is 'builtins.str'
+    await f()
+
+async def h() -> None:
+    g = gen()
+    await g.asend(())  # E: Argument 1 to "asend" of "AsyncGenerator" has incompatible type "Tuple[]"; expected "str"
+    reveal_type(await g.asend('hello'))  # E: Revealed type is 'builtins.int*'
+
+[builtins fixtures/dict.pyi]
+
+[case testAsyncGeneratorAthrow]
+# flags: --fast-parser --python-version 3.6
+from typing import AsyncGenerator
+
+async def gen() -> AsyncGenerator[str, int]:
+    try:
+        yield 'hello'
+    except BaseException:
+        yield 'world'
+
+async def h() -> None:
+    g = gen()
+    v = await g.asend(1)
+    reveal_type(v)  # E: Revealed type is 'builtins.str*'
+    reveal_type(await g.athrow(BaseException))  # E: Revealed type is 'builtins.str*'
+
+[builtins fixtures/dict.pyi]
+
+[case testAsyncGeneratorNoSyncIteration]
+# flags: --fast-parser --python-version 3.6
+from typing import AsyncGenerator
+
+async def gen() -> AsyncGenerator[int, None]:
+    for i in (1, 2, 3):
+        yield i
+
+def h() -> None:
+    for i in gen():
+        pass
+
+[builtins fixtures/dict.pyi]
+
+[out]
+main:9: error: Iterable expected
+main:9: error: AsyncGenerator[int, None] has no attribute "__iter__"; maybe "__aiter__"?
+
+[case testAsyncGeneratorNoYieldFrom]
+# flags: --fast-parser --python-version 3.6
+from typing import AsyncGenerator
+
+async def f() -> AsyncGenerator[int, None]:
+    pass
+
+async def gen() -> AsyncGenerator[int, None]:
+    yield from f()  # E: 'yield from' in async function
+
+[builtins fixtures/dict.pyi]
+
+[case testAsyncGeneratorNoReturnWithValue]
+# flags: --fast-parser --python-version 3.6
+from typing import AsyncGenerator
+
+async def return_int() -> AsyncGenerator[int, None]:
+    yield 1
+    return 42  # E: 'return' with value in async generator is not allowed
+
+async def return_none() -> AsyncGenerator[int, None]:
+    yield 1
+    return None  # E: 'return' with value in async generator is not allowed
+
+def f() -> None:
+    return
+
+async def return_f() -> AsyncGenerator[int, None]:
+    yield 1
+    return f()  # E: 'return' with value in async generator is not allowed
+
+[builtins fixtures/dict.pyi]
 
 -- The full matrix of coroutine compatibility
 -- ------------------------------------------
diff --git a/test-data/unit/fixtures/dict.pyi b/test-data/unit/fixtures/dict.pyi
index d36145fa0654..dc89366c1133 100644
--- a/test-data/unit/fixtures/dict.pyi
+++ b/test-data/unit/fixtures/dict.pyi
@@ -38,3 +38,5 @@ class tuple: pass
 class function: pass
 class float: pass
 class bool: pass
+
+class BaseException: pass
diff --git a/test-data/unit/lib-stub/typing.pyi b/test-data/unit/lib-stub/typing.pyi
index 0377f19a1e5d..8d252dbddf2e 100644
--- a/test-data/unit/lib-stub/typing.pyi
+++ b/test-data/unit/lib-stub/typing.pyi
@@ -59,6 +59,22 @@ class Generator(Iterator[T], Generic[T, U, V]):
     @abstractmethod
     def __iter__(self) -> 'Generator[T, U, V]': pass
 
+class AsyncGenerator(AsyncIterator[T], Generic[T, U]):
+    @abstractmethod
+    def __anext__(self) -> Awaitable[T]: pass
+
+    @abstractmethod
+    def asend(self, value: U) -> Awaitable[T]: pass
+
+    @abstractmethod
+    def athrow(self, typ: Any, val: Any=None, tb: Any=None) -> Awaitable[T]: pass
+
+    @abstractmethod
+    def aclose(self) -> Awaitable[T]: pass
+
+    @abstractmethod
+    def __aiter__(self) -> 'AsyncGenerator[T, U]': pass
+
 class Awaitable(Generic[T]):
     @abstractmethod
     def __await__(self) -> Generator[Any, Any, T]: pass