diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 1125da4..c31669a 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -13,11 +13,9 @@ jobs:
       max-parallel: 5
       matrix:
         python-version:
-        - 2.7
         - 3.6
         - 3.7
         - 3.8
-        - pypy2
         - pypy3
 
     steps:
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index b9eccd9..45a1ebf 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -70,10 +70,10 @@ other hand, the following are all very welcome:
   tox
   ```
 
-  But note that: (1) this will print slightly misleading coverage
+  But note that: (1) this might print slightly misleading coverage
   statistics, because it only shows coverage for individual python
-  versions, and there are some lines that are only executed on python
-  2 or only executed on python 3, and (2) the full test suite will
+  versions, and there might be some lines that are only executed on some
+  python versions or implementations, and (2) the full test suite will
   automatically get run when you submit a pull request, so you don't
   need to worry too much about tracking down a version of cpython 3.3
   or whatever just to run the tests.
diff --git a/README.rst b/README.rst
index 74bb182..f998b01 100644
--- a/README.rst
+++ b/README.rst
@@ -112,7 +112,8 @@ library.
 It has a test suite with 100.0% coverage for both statements and
 branches.
 
-Currently it supports Python 3 (testing on 3.5-3.8), Python 2.7, and PyPy.
+Currently it supports Python 3 (testing on 3.5-3.8) and PyPy 3.
+The last Python 2-compatible version was h11 0.11.x.
 (Originally it had a Cython wrapper for `http-parser
 <https://github.com/nodejs/http-parser>`_ and a beautiful nested state
 machine implemented with ``yield from`` to postprocess the output. But
diff --git a/bench/asv.conf.json b/bench/asv.conf.json
index f65e4dd..0a07c42 100644
--- a/bench/asv.conf.json
+++ b/bench/asv.conf.json
@@ -36,7 +36,7 @@
 
     // The Pythons you'd like to test against.  If not provided, defaults
     // to the current version of Python used to run `asv`.
-    "pythons": ["2.7", "3.5", "pypy"],
+    "pythons": ["3.8", "pypy3"],
 
     // The matrix of dependencies to test.  Each key is the name of a
     // package (in PyPI) and the values are version numbers.  An empty
diff --git a/docs/source/index.rst b/docs/source/index.rst
index c08b76d..617638f 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -44,7 +44,9 @@ whatever. But h11 makes it much easier to implement something like
 Vital statistics
 ----------------
 
-* Requirements: Python 2.7 or Python 3.5+ (PyPy works great)
+* Requirements: Python 3.5+ (PyPy works great)
+
+  The last Python 2-compatible version was h11 0.11.x.
 
 * Install: ``pip install h11``
 
diff --git a/fuzz/afl-server.py b/fuzz/afl-server.py
index 450c68b..0ff1947 100644
--- a/fuzz/afl-server.py
+++ b/fuzz/afl-server.py
@@ -9,11 +9,6 @@
 
 import h11
 
-if sys.version_info[0] >= 3:
-    in_file = sys.stdin.detach()
-else:
-    in_file = sys.stdin
-
 
 def process_all(c):
     while True:
@@ -26,7 +21,7 @@ def process_all(c):
 
 afl.init()
 
-data = in_file.read()
+data = sys.stdin.detach().read()
 
 # one big chunk
 server1 = h11.Connection(h11.SERVER)
diff --git a/h11/_connection.py b/h11/_connection.py
index 410c4e9..b6f8760 100644
--- a/h11/_connection.py
+++ b/h11/_connection.py
@@ -109,7 +109,7 @@ def _body_framing(request_method, event):
 ################################################################
 
 
-class Connection(object):
+class Connection:
     """An object encapsulating the state of an HTTP connection.
 
     Args:
diff --git a/h11/_events.py b/h11/_events.py
index c11d838..1827930 100644
--- a/h11/_events.py
+++ b/h11/_events.py
@@ -24,7 +24,7 @@
 request_target_re = re.compile(request_target.encode("ascii"))
 
 
-class _EventBundle(object):
+class _EventBundle:
     _fields = []
     _defaults = {}
 
@@ -85,9 +85,6 @@ def __repr__(self):
     def __eq__(self, other):
         return self.__class__ == other.__class__ and self.__dict__ == other.__dict__
 
-    def __ne__(self, other):
-        return not self.__eq__(other)
-
     # This is an unhashable type.
     __hash__ = None
 
diff --git a/h11/_headers.py b/h11/_headers.py
index 5229ac4..7ed39bc 100644
--- a/h11/_headers.py
+++ b/h11/_headers.py
@@ -132,7 +132,7 @@ def normalize_and_validate(headers, _parsed=False):
         raw_name = name
         name = name.lower()
         if name == b"content-length":
-            lengths = set(length.strip() for length in value.split(b","))
+            lengths = {length.strip() for length in value.split(b",")}
             if len(lengths) != 1:
                 raise LocalProtocolError("conflicting Content-Length headers")
             value = lengths.pop()
diff --git a/h11/_readers.py b/h11/_readers.py
index cc86bff..75f00bc 100644
--- a/h11/_readers.py
+++ b/h11/_readers.py
@@ -54,13 +54,7 @@ def _obsolete_line_fold(lines):
 
 def _decode_header_lines(lines):
     for line in _obsolete_line_fold(lines):
-        # _obsolete_line_fold yields either bytearray or bytes objects. On
-        # Python 3, validate() takes either and returns matches as bytes. But
-        # on Python 2, validate can return matches as bytearrays, so we have
-        # to explicitly cast back.
-        matches = validate(
-            header_field_re, bytes(line), "illegal header line: {!r}", bytes(line)
-        )
+        matches = validate(header_field_re, line, "illegal header line: {!r}", line)
         yield (matches["field_name"], matches["field_value"])
 
 
@@ -127,7 +121,7 @@ def read_eof(self):
 chunk_header_re = re.compile(chunk_header.encode("ascii"))
 
 
-class ChunkedReader(object):
+class ChunkedReader:
     def __init__(self):
         self._bytes_in_chunk = 0
         # After reading a chunk, we have to throw away the trailing \r\n; if
@@ -163,9 +157,7 @@ def __call__(self, buf):
                 chunk_header,
             )
             # XX FIXME: we discard chunk extensions. Does anyone care?
-            # We convert to bytes because Python 2's `int()` function doesn't
-            # work properly on bytearray objects.
-            self._bytes_in_chunk = int(bytes(matches["chunk_size"]), base=16)
+            self._bytes_in_chunk = int(matches["chunk_size"], base=16)
             if self._bytes_in_chunk == 0:
                 self._reading_trailer = True
                 return self(buf)
@@ -191,7 +183,7 @@ def read_eof(self):
         )
 
 
-class Http10Reader(object):
+class Http10Reader:
     def __call__(self, buf):
         data = buf.maybe_extract_at_most(999999999)
         if data is None:
diff --git a/h11/_receivebuffer.py b/h11/_receivebuffer.py
index c56749a..8b709df 100644
--- a/h11/_receivebuffer.py
+++ b/h11/_receivebuffer.py
@@ -1,5 +1,3 @@
-import sys
-
 __all__ = ["ReceiveBuffer"]
 
 
@@ -38,7 +36,7 @@
 # slightly clever thing where we delay calling compress() until we've
 # processed a whole event, which could in theory be slightly more efficient
 # than the internal bytearray support.)
-class ReceiveBuffer(object):
+class ReceiveBuffer:
     def __init__(self):
         self._data = bytearray()
         # These are both absolute offsets into self._data:
@@ -53,10 +51,6 @@ def __bool__(self):
     def __bytes__(self):
         return bytes(self._data[self._start :])
 
-    if sys.version_info[0] < 3:  # version specific: Python 2
-        __str__ = __bytes__
-        __nonzero__ = __bool__
-
     def __len__(self):
         return len(self._data) - self._start
 
diff --git a/h11/_state.py b/h11/_state.py
index 70a5e04..0f08a09 100644
--- a/h11/_state.py
+++ b/h11/_state.py
@@ -197,7 +197,7 @@
 }
 
 
-class ConnectionState(object):
+class ConnectionState:
     def __init__(self):
         # Extra bits of state that don't quite fit into the state model.
 
diff --git a/h11/_util.py b/h11/_util.py
index 0a2c28e..eb1a5cd 100644
--- a/h11/_util.py
+++ b/h11/_util.py
@@ -1,6 +1,3 @@
-import re
-import sys
-
 __all__ = [
     "ProtocolError",
     "LocalProtocolError",
@@ -74,34 +71,17 @@ def _reraise_as_remote_protocol_error(self):
         # (exc_info[0]) separately from the exception object (exc_info[1]),
         # and we only modified the latter. So we really do need to re-raise
         # the new type explicitly.
-        if sys.version_info[0] >= 3:
-            # On py3, the traceback is part of the exception object, so our
-            # in-place modification preserved it and we can just re-raise:
-            raise self
-        else:
-            # On py2, preserving the traceback requires 3-argument
-            # raise... but on py3 this is a syntax error, so we have to hide
-            # it inside an exec
-            exec("raise RemoteProtocolError, self, sys.exc_info()[2]")
+        # On py3, the traceback is part of the exception object, so our
+        # in-place modification preserved it and we can just re-raise:
+        raise self
 
 
 class RemoteProtocolError(ProtocolError):
     pass
 
 
-try:
-    _fullmatch = type(re.compile("")).fullmatch
-except AttributeError:
-
-    def _fullmatch(regex, data):  # version specific: Python < 3.4
-        match = regex.match(data)
-        if match and match.end() != len(data):
-            match = None
-        return match
-
-
 def validate(regex, data, msg="malformed data", *format_args):
-    match = _fullmatch(regex, data)
+    match = regex.fullmatch(data)
     if not match:
         if format_args:
             msg = msg.format(*format_args)
diff --git a/h11/_writers.py b/h11/_writers.py
index 7531579..cb5e8a8 100644
--- a/h11/_writers.py
+++ b/h11/_writers.py
@@ -7,32 +7,12 @@
 # - a writer
 # - or, for body writers, a dict of framin-dependent writer factories
 
-import sys
-
 from ._events import Data, EndOfMessage
 from ._state import CLIENT, IDLE, SEND_BODY, SEND_RESPONSE, SERVER
 from ._util import LocalProtocolError
 
 __all__ = ["WRITERS"]
 
-# Equivalent of bstr % values, that works on python 3.x for x < 5
-if (3, 0) <= sys.version_info < (3, 5):
-
-    def bytesmod(bstr, values):
-        decoded_values = []
-        for value in values:
-            if isinstance(value, bytes):
-                decoded_values.append(value.decode("ascii"))
-            else:
-                decoded_values.append(value)
-        return (bstr.decode("ascii") % tuple(decoded_values)).encode("ascii")
-
-
-else:
-
-    def bytesmod(bstr, values):
-        return bstr % values
-
 
 def write_headers(headers, write):
     # "Since the Host field-value is critical information for handling a
@@ -41,17 +21,17 @@ def write_headers(headers, write):
     raw_items = headers._full_items
     for raw_name, name, value in raw_items:
         if name == b"host":
-            write(bytesmod(b"%s: %s\r\n", (raw_name, value)))
+            write(b"%s: %s\r\n" % (raw_name, value))
     for raw_name, name, value in raw_items:
         if name != b"host":
-            write(bytesmod(b"%s: %s\r\n", (raw_name, value)))
+            write(b"%s: %s\r\n" % (raw_name, value))
     write(b"\r\n")
 
 
 def write_request(request, write):
     if request.http_version != b"1.1":
         raise LocalProtocolError("I only send HTTP/1.1")
-    write(bytesmod(b"%s %s HTTP/1.1\r\n", (request.method, request.target)))
+    write(b"%s %s HTTP/1.1\r\n" % (request.method, request.target))
     write_headers(request.headers, write)
 
 
@@ -68,11 +48,11 @@ def write_any_response(response, write):
     # from stdlib's http.HTTPStatus table. Or maybe just steal their enums
     # (either by import or copy/paste). We already accept them as status codes
     # since they're of type IntEnum < int.
-    write(bytesmod(b"HTTP/1.1 %s %s\r\n", (status_bytes, response.reason)))
+    write(b"HTTP/1.1 %s %s\r\n" % (status_bytes, response.reason))
     write_headers(response.headers, write)
 
 
-class BodyWriter(object):
+class BodyWriter:
     def __call__(self, event, write):
         if type(event) is Data:
             self.send_data(event.data, write)
@@ -111,7 +91,7 @@ def send_data(self, data, write):
         # end-of-message.
         if not data:
             return
-        write(bytesmod(b"%x\r\n", (len(data),)))
+        write(b"%x\r\n" % len(data))
         write(data)
         write(b"\r\n")
 
diff --git a/h11/tests/test_against_stdlib_http.py b/h11/tests/test_against_stdlib_http.py
index b4219ff..e6c5db4 100644
--- a/h11/tests/test_against_stdlib_http.py
+++ b/h11/tests/test_against_stdlib_http.py
@@ -1,26 +1,14 @@
 import json
 import os.path
 import socket
+import socketserver
 import threading
 from contextlib import closing, contextmanager
+from http.server import SimpleHTTPRequestHandler
+from urllib.request import urlopen
 
 import h11
 
-try:
-    from urllib.request import urlopen
-except ImportError:  # version specific: Python 2
-    from urllib2 import urlopen
-
-try:
-    import socketserver
-except ImportError:  # version specific: Python 2
-    import SocketServer as socketserver
-
-try:
-    from http.server import SimpleHTTPRequestHandler
-except ImportError:  # version specific: Python 2
-    from SimpleHTTPServer import SimpleHTTPRequestHandler
-
 
 @contextmanager
 def socket_server(handler):
diff --git a/h11/tests/test_events.py b/h11/tests/test_events.py
index 07ffc13..e20f741 100644
--- a/h11/tests/test_events.py
+++ b/h11/tests/test_events.py
@@ -1,3 +1,5 @@
+from http import HTTPStatus
+
 import pytest
 
 from .. import _events
@@ -154,10 +156,6 @@ def test_events():
 
 def test_intenum_status_code():
     # https://github.com/python-hyper/h11/issues/72
-    try:
-        from http import HTTPStatus
-    except ImportError:
-        pytest.skip("Only affects Python 3")
 
     r = Response(status_code=HTTPStatus.OK, headers=[], http_version="1.0")
     assert r.status_code == HTTPStatus.OK
diff --git a/h11/tests/test_util.py b/h11/tests/test_util.py
index 74ab33b..d851bdc 100644
--- a/h11/tests/test_util.py
+++ b/h11/tests/test_util.py
@@ -93,7 +93,7 @@ def test_bytesify():
     assert bytesify("123") == b"123"
 
     with pytest.raises(UnicodeEncodeError):
-        bytesify(u"\u1234")
+        bytesify("\u1234")
 
     with pytest.raises(TypeError):
         bytesify(10)
diff --git a/newsfragments/114.removal.rst b/newsfragments/114.removal.rst
new file mode 100644
index 0000000..849b82c
--- /dev/null
+++ b/newsfragments/114.removal.rst
@@ -0,0 +1,2 @@
+Python 2.7 and PyPy 2 support is removed. h11 now requires Python>=3.5 including PyPy 3.
+Users running `pip install h11` on Python 2 will automatically get the last Python 2-compatible version.
diff --git a/setup.cfg b/setup.cfg
index bda6834..0bd1262 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -1,6 +1,3 @@
-[bdist_wheel]
-universal=1
-
 [isort]
 combine_as_imports=True
 force_grid_wrap=0
diff --git a/setup.py b/setup.py
index 25cbbe8..024b9a3 100644
--- a/setup.py
+++ b/setup.py
@@ -17,15 +17,15 @@
     # This means, just install *everything* you see under h11/, even if it
     # doesn't look like a source file, so long as it appears in MANIFEST.in:
     include_package_data=True,
+    python_requires=">=3.5",
     classifiers=[
         "Development Status :: 3 - Alpha",
         "Intended Audience :: Developers",
         "License :: OSI Approved :: MIT License",
         "Programming Language :: Python :: Implementation :: CPython",
         "Programming Language :: Python :: Implementation :: PyPy",
-        "Programming Language :: Python :: 2",
-        "Programming Language :: Python :: 2.7",
         "Programming Language :: Python :: 3",
+        "Programming Language :: Python :: 3 :: Only",
         "Programming Language :: Python :: 3.5",
         "Programming Language :: Python :: 3.6",
         "Programming Language :: Python :: 3.7",
diff --git a/tox.ini b/tox.ini
index de9b566..c2c748e 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,13 +1,11 @@
 [tox]
-envlist = format, py27, py36, py37, py38, pypy, pypy3
+envlist = format, py36, py37, py38, pypy3
 
 [gh-actions]
 python =
-    2.7: py27
     3.6: py36
     3.7: py37
     3.8: py38, format
-    pypy2: pypy
     pypy3: pypy3
 
 [testenv]