diff --git a/asyncpg/connection.py b/asyncpg/connection.py
index 8e841871..43339346 100644
--- a/asyncpg/connection.py
+++ b/asyncpg/connection.py
@@ -14,6 +14,7 @@
 import sys
 import time
 import traceback
+import typing
 import warnings
 
 from . import compat
@@ -25,6 +26,7 @@
 from . import protocol
 from . import serverversion
 from . import transaction
+from . import types
 from . import utils
 
 
@@ -179,11 +181,11 @@ def remove_log_listener(self, callback):
         """
         self._log_listeners.discard(callback)
 
-    def get_server_pid(self):
+    def get_server_pid(self) -> int:
         """Return the PID of the Postgres server the connection is bound to."""
         return self._protocol.get_server_pid()
 
-    def get_server_version(self):
+    def get_server_version(self) -> types.ServerVersion:
         """Return the version of the connected PostgreSQL server.
 
         The returned value is a named tuple similar to that in
@@ -199,7 +201,7 @@ def get_server_version(self):
         """
         return self._server_version
 
-    def get_settings(self):
+    def get_settings(self) -> protocol.ConnectionSettings:
         """Return connection settings.
 
         :return: :class:`~asyncpg.ConnectionSettings`.
@@ -207,7 +209,7 @@ def get_settings(self):
         return self._protocol.get_settings()
 
     def transaction(self, *, isolation='read_committed', readonly=False,
-                    deferrable=False):
+                    deferrable=False) -> transaction.Transaction:
         """Create a :class:`~transaction.Transaction` object.
 
         Refer to `PostgreSQL documentation`_ on the meaning of transaction
@@ -230,7 +232,7 @@ def transaction(self, *, isolation='read_committed', readonly=False,
         self._check_open()
         return transaction.Transaction(self, isolation, readonly, deferrable)
 
-    def is_in_transaction(self):
+    def is_in_transaction(self) -> bool:
         """Return True if Connection is currently inside a transaction.
 
         :return bool: True if inside transaction, False otherwise.
@@ -275,7 +277,8 @@ async def execute(self, query: str, *args, timeout: float=None) -> str:
         _, status, _ = await self._execute(query, args, 0, timeout, True)
         return status.decode()
 
-    async def executemany(self, command: str, args, *, timeout: float=None):
+    async def executemany(self, command: str, args, *, timeout: float=None) \
+            -> None:
         """Execute an SQL *command* for each sequence of arguments in *args*.
 
         Example:
@@ -378,7 +381,8 @@ async def _introspect_types(self, typeoids, timeout):
         return await self.__execute(
             self._intro_query, (list(typeoids),), 0, timeout)
 
-    def cursor(self, query, *args, prefetch=None, timeout=None):
+    def cursor(self, query, *args, prefetch=None, timeout=None) \
+            -> cursor.CursorFactory:
         """Return a *cursor factory* for the specified query.
 
         :param args: Query arguments.
@@ -392,7 +396,8 @@ def cursor(self, query, *args, prefetch=None, timeout=None):
         return cursor.CursorFactory(self, query, None, args,
                                     prefetch, timeout)
 
-    async def prepare(self, query, *, timeout=None):
+    async def prepare(self, query, *, timeout=None) \
+            -> prepared_stmt.PreparedStatement:
         """Create a *prepared statement* for the specified query.
 
         :param str query: Text of the query to create a prepared statement for.
@@ -408,7 +413,8 @@ async def _prepare(self, query, *, timeout=None, use_cache: bool=False):
                                          use_cache=use_cache)
         return prepared_stmt.PreparedStatement(self, query, stmt)
 
-    async def fetch(self, query, *args, timeout=None) -> list:
+    async def fetch(self, query, *args, timeout=None) \
+            -> typing.List[protocol.Record]:
         """Run a query and return the results as a list of :class:`Record`.
 
         :param str query: Query text.
@@ -420,7 +426,8 @@ async def fetch(self, query, *args, timeout=None) -> list:
         self._check_open()
         return await self._execute(query, args, 0, timeout)
 
-    async def fetchval(self, query, *args, column=0, timeout=None):
+    async def fetchval(self, query, *args, column=0, timeout=None) \
+            -> typing.Any:
         """Run a query and return a value in the first row.
 
         :param str query: Query text.
@@ -441,7 +448,8 @@ async def fetchval(self, query, *args, column=0, timeout=None):
             return None
         return data[0][column]
 
-    async def fetchrow(self, query, *args, timeout=None):
+    async def fetchrow(self, query, *args, timeout=None) \
+            -> typing.Optional[protocol.Record]:
         """Run a query and return the first row.
 
         :param str query: Query text
@@ -461,7 +469,8 @@ async def copy_from_table(self, table_name, *, output,
                               columns=None, schema_name=None, timeout=None,
                               format=None, oids=None, delimiter=None,
                               null=None, header=None, quote=None,
-                              escape=None, force_quote=None, encoding=None):
+                              escape=None, force_quote=None, encoding=None) \
+            -> str:
         """Copy table contents to a file or file-like object.
 
         :param str table_name:
@@ -533,7 +542,7 @@ async def copy_from_query(self, query, *args, output,
                               timeout=None, format=None, oids=None,
                               delimiter=None, null=None, header=None,
                               quote=None, escape=None, force_quote=None,
-                              encoding=None):
+                              encoding=None) -> str:
         """Copy the results of a query to a file or file-like object.
 
         :param str query:
@@ -597,7 +606,7 @@ async def copy_to_table(self, table_name, *, source,
                             delimiter=None, null=None, header=None,
                             quote=None, escape=None, force_quote=None,
                             force_not_null=None, force_null=None,
-                            encoding=None):
+                            encoding=None) -> str:
         """Copy data to the specified table.
 
         :param str table_name:
@@ -668,7 +677,7 @@ async def copy_to_table(self, table_name, *, source,
 
     async def copy_records_to_table(self, table_name, *, records,
                                     columns=None, schema_name=None,
-                                    timeout=None):
+                                    timeout=None) -> str:
         """Copy a list of records to the specified table using binary COPY.
 
         :param str table_name:
@@ -1060,7 +1069,7 @@ async def set_builtin_type_codec(self, typename, *,
         # Statement cache is no longer valid due to codec changes.
         self._drop_local_statement_cache()
 
-    def is_closed(self):
+    def is_closed(self) -> bool:
         """Return ``True`` if the connection is closed, ``False`` otherwise.
 
         :return bool: ``True`` if the connection is closed, ``False``
@@ -1503,7 +1512,7 @@ async def connect(dsn=None, *,
                   command_timeout=None,
                   ssl=None,
                   connection_class=Connection,
-                  server_settings=None):
+                  server_settings=None) -> Connection:
     r"""A coroutine to establish a connection to a PostgreSQL server.
 
     The connection parameters may be specified either as a connection
diff --git a/asyncpg/cursor.py b/asyncpg/cursor.py
index 030def0e..56c289c0 100644
--- a/asyncpg/cursor.py
+++ b/asyncpg/cursor.py
@@ -6,10 +6,12 @@
 
 
 import collections
+import typing
 
 from . import compat
 from . import connresource
 from . import exceptions
+from . import protocol
 
 
 class CursorFactory(connresource.ConnectionResource):
@@ -33,7 +35,7 @@ def __init__(self, connection, query, state, args, prefetch, timeout):
 
     @compat.aiter_compat
     @connresource.guarded
-    def __aiter__(self):
+    def __aiter__(self) -> 'CursorIterator':
         prefetch = 50 if self._prefetch is None else self._prefetch
         return CursorIterator(self._connection,
                               self._query, self._state,
@@ -41,7 +43,7 @@ def __aiter__(self):
                               self._timeout)
 
     @connresource.guarded
-    def __await__(self):
+    def __await__(self) -> 'Cursor':
         if self._prefetch is not None:
             raise exceptions.InterfaceError(
                 'prefetch argument can only be specified for iterable cursor')
@@ -164,11 +166,11 @@ def __init__(self, connection, query, state, args, prefetch, timeout):
 
     @compat.aiter_compat
     @connresource.guarded
-    def __aiter__(self):
+    def __aiter__(self) -> 'CursorIterator':
         return self
 
     @connresource.guarded
-    async def __anext__(self):
+    async def __anext__(self) -> protocol.Record:
         if self._state is None:
             self._state = await self._connection._get_statement(
                 self._query, self._timeout, named=True)
@@ -203,7 +205,7 @@ async def _init(self, timeout):
         return self
 
     @connresource.guarded
-    async def fetch(self, n, *, timeout=None):
+    async def fetch(self, n, *, timeout=None) -> typing.List[protocol.Record]:
         r"""Return the next *n* rows as a list of :class:`Record` objects.
 
         :param float timeout: Optional timeout value in seconds.
@@ -221,7 +223,7 @@ async def fetch(self, n, *, timeout=None):
         return recs
 
     @connresource.guarded
-    async def fetchrow(self, *, timeout=None):
+    async def fetchrow(self, *, timeout=None) -> protocol.Record:
         r"""Return the next row.
 
         :param float timeout: Optional timeout value in seconds.
diff --git a/asyncpg/pool.py b/asyncpg/pool.py
index 64f4071e..d103b429 100644
--- a/asyncpg/pool.py
+++ b/asyncpg/pool.py
@@ -10,11 +10,13 @@
 import inspect
 import logging
 import time
+import typing
 import warnings
 
 from . import connection
 from . import connect_utils
 from . import exceptions
+from . import protocol
 
 
 logger = logging.getLogger(__name__)
@@ -508,7 +510,8 @@ async def execute(self, query: str, *args, timeout: float=None) -> str:
         async with self.acquire() as con:
             return await con.execute(query, *args, timeout=timeout)
 
-    async def executemany(self, command: str, args, *, timeout: float=None):
+    async def executemany(self, command: str, args, *, timeout: float=None) \
+            -> None:
         """Execute an SQL *command* for each sequence of arguments in *args*.
 
         Pool performs this operation using one of its connections.  Other than
@@ -520,7 +523,8 @@ async def executemany(self, command: str, args, *, timeout: float=None):
         async with self.acquire() as con:
             return await con.executemany(command, args, timeout=timeout)
 
-    async def fetch(self, query, *args, timeout=None) -> list:
+    async def fetch(self, query, *args, timeout=None) \
+            -> typing.List[protocol.Record]:
         """Run a query and return the results as a list of :class:`Record`.
 
         Pool performs this operation using one of its connections.  Other than
@@ -532,7 +536,8 @@ async def fetch(self, query, *args, timeout=None) -> list:
         async with self.acquire() as con:
             return await con.fetch(query, *args, timeout=timeout)
 
-    async def fetchval(self, query, *args, column=0, timeout=None):
+    async def fetchval(self, query, *args, column=0, timeout=None) \
+            -> typing.Any:
         """Run a query and return a value in the first row.
 
         Pool performs this operation using one of its connections.  Other than
@@ -545,7 +550,8 @@ async def fetchval(self, query, *args, column=0, timeout=None):
             return await con.fetchval(
                 query, *args, column=column, timeout=timeout)
 
-    async def fetchrow(self, query, *args, timeout=None):
+    async def fetchrow(self, query, *args, timeout=None) \
+            -> typing.Optional[protocol.Record]:
         """Run a query and return the first row.
 
         Pool performs this operation using one of its connections.  Other than
@@ -557,7 +563,7 @@ async def fetchrow(self, query, *args, timeout=None):
         async with self.acquire() as con:
             return await con.fetchrow(query, *args, timeout=timeout)
 
-    def acquire(self, *, timeout=None):
+    def acquire(self, *, timeout=None) -> connection.Connection:
         """Acquire a database connection from the pool.
 
         :param float timeout: A timeout for acquiring a Connection.
@@ -784,7 +790,7 @@ def create_pool(dsn=None, *,
                 init=None,
                 loop=None,
                 connection_class=connection.Connection,
-                **connect_kwargs):
+                **connect_kwargs) -> Pool:
     r"""Create a connection pool.
 
     Can be used either with an ``async with`` block:
diff --git a/asyncpg/prepared_stmt.py b/asyncpg/prepared_stmt.py
index 09a0a2ec..a459b200 100644
--- a/asyncpg/prepared_stmt.py
+++ b/asyncpg/prepared_stmt.py
@@ -6,10 +6,13 @@
 
 
 import json
+import typing
 
 from . import connresource
 from . import cursor
 from . import exceptions
+from . import protocol
+from . import types
 
 
 class PreparedStatement(connresource.ConnectionResource):
@@ -50,7 +53,7 @@ def get_statusmsg(self) -> str:
         return self._last_status.decode()
 
     @connresource.guarded
-    def get_parameters(self):
+    def get_parameters(self) -> typing.Tuple[types.Type, ...]:
         """Return a description of statement parameters types.
 
         :return: A tuple of :class:`asyncpg.types.Type`.
@@ -67,7 +70,7 @@ def get_parameters(self):
         return self._state._get_parameters()
 
     @connresource.guarded
-    def get_attributes(self):
+    def get_attributes(self) -> typing.Tuple[types.Attribute, ...]:
         """Return a description of relation attributes (columns).
 
         :return: A tuple of :class:`asyncpg.types.Attribute`.
@@ -108,7 +111,7 @@ def cursor(self, *args, prefetch=None,
                                     timeout)
 
     @connresource.guarded
-    async def explain(self, *args, analyze=False):
+    async def explain(self, *args, analyze=False) -> typing.Dict:
         """Return the execution plan of the statement.
 
         :param args: Query arguments.
@@ -150,7 +153,7 @@ async def explain(self, *args, analyze=False):
         return json.loads(data)
 
     @connresource.guarded
-    async def fetch(self, *args, timeout=None):
+    async def fetch(self, *args, timeout=None) -> typing.List[protocol.Record]:
         r"""Execute the statement and return a list of :class:`Record` objects.
 
         :param str query: Query text
@@ -163,7 +166,7 @@ async def fetch(self, *args, timeout=None):
         return data
 
     @connresource.guarded
-    async def fetchval(self, *args, column=0, timeout=None):
+    async def fetchval(self, *args, column=0, timeout=None) -> typing.Any:
         """Execute the statement and return a value in the first row.
 
         :param args: Query arguments.
@@ -182,7 +185,8 @@ async def fetchval(self, *args, column=0, timeout=None):
         return data[0][column]
 
     @connresource.guarded
-    async def fetchrow(self, *args, timeout=None):
+    async def fetchrow(self, *args, timeout=None) \
+            -> typing.Optional[protocol.Record]:
         """Execute the statement and return the first row.
 
         :param str query: Query text
diff --git a/asyncpg/protocol/__init__.py b/asyncpg/protocol/__init__.py
index e872e2fa..16186260 100644
--- a/asyncpg/protocol/__init__.py
+++ b/asyncpg/protocol/__init__.py
@@ -5,4 +5,4 @@
 # the Apache 2.0 License: http://www.apache.org/licenses/LICENSE-2.0
 
 
-from .protocol import Protocol, Record, NO_TIMEOUT  # NOQA
+from .protocol import Protocol, Record, ConnectionSettings, NO_TIMEOUT  # NOQA