diff --git a/django/contrib/admindocs/views.py b/django/contrib/admindocs/views.py
index 35aad4c897..543b3e6b02 100644
--- a/django/contrib/admindocs/views.py
+++ b/django/contrib/admindocs/views.py
@@ -14,6 +14,7 @@ from django.db import models
 from django.http import Http404
 from django.template.engine import Engine
 from django.utils.decorators import method_decorator
+from django.utils.inspect import func_has_no_args
 from django.utils.translation import ugettext as _
 from django.views.generic import TemplateView
 
@@ -243,7 +244,7 @@ class ModelDetailView(BaseAdminDocsView):
 
         # Gather model methods.
         for func_name, func in model.__dict__.items():
-            if (inspect.isfunction(func) and len(inspect.getargspec(func)[0]) == 1):
+            if inspect.isfunction(func) and func_has_no_args(func):
                 try:
                     for exclude in MODEL_METHODS_EXCLUDE:
                         if func_name.startswith(exclude):
diff --git a/django/contrib/gis/management/commands/ogrinspect.py b/django/contrib/gis/management/commands/ogrinspect.py
index 1194cf6cfb..f161c06e89 100644
--- a/django/contrib/gis/management/commands/ogrinspect.py
+++ b/django/contrib/gis/management/commands/ogrinspect.py
@@ -1,8 +1,8 @@
 import argparse
-import inspect
 
 from django.contrib.gis import gdal
 from django.core.management.base import BaseCommand, CommandError
+from django.utils.inspect import get_func_args
 
 
 class LayerOptionAction(argparse.Action):
@@ -91,7 +91,7 @@ class Command(BaseCommand):
         from django.contrib.gis.utils.ogrinspect import _ogrinspect, mapping
         # Filter options to params accepted by `_ogrinspect`
         ogr_options = {k: v for k, v in options.items()
-                       if k in inspect.getargspec(_ogrinspect).args and v is not None}
+                       if k in get_func_args(_ogrinspect) and v is not None}
         output = [s for s in _ogrinspect(ds, model_name, **ogr_options)]
 
         if options['mapping']:
diff --git a/django/core/files/storage.py b/django/core/files/storage.py
index 65b6d46463..554f05f2a9 100644
--- a/django/core/files/storage.py
+++ b/django/core/files/storage.py
@@ -2,7 +2,6 @@ import errno
 import os
 import warnings
 from datetime import datetime
-from inspect import getargspec
 
 from django.conf import settings
 from django.core.exceptions import SuspiciousFileOperation
@@ -14,6 +13,7 @@ from django.utils.deconstruct import deconstructible
 from django.utils.deprecation import RemovedInDjango20Warning
 from django.utils.encoding import filepath_to_uri, force_text
 from django.utils.functional import LazyObject
+from django.utils.inspect import func_supports_parameter
 from django.utils.module_loading import import_string
 from django.utils.six.moves.urllib.parse import urljoin
 from django.utils.text import get_valid_filename
@@ -49,8 +49,7 @@ class Storage(object):
         if not hasattr(content, 'chunks'):
             content = File(content)
 
-        args, varargs, varkw, defaults = getargspec(self.get_available_name)
-        if 'max_length' in args:
+        if func_supports_parameter(self.get_available_name, 'max_length'):
             name = self.get_available_name(name, max_length=max_length)
         else:
             warnings.warn(
diff --git a/django/db/migrations/writer.py b/django/db/migrations/writer.py
index a0832ff4f6..a7848d744f 100644
--- a/django/db/migrations/writer.py
+++ b/django/db/migrations/writer.py
@@ -3,7 +3,6 @@ from __future__ import unicode_literals
 import collections
 import datetime
 import decimal
-import inspect
 import math
 import os
 import re
@@ -18,6 +17,7 @@ from django.utils import datetime_safe, six
 from django.utils._os import upath
 from django.utils.encoding import force_text
 from django.utils.functional import Promise
+from django.utils.inspect import get_func_args
 from django.utils.module_loading import module_dir
 from django.utils.timezone import utc
 from django.utils.version import get_docs_version
@@ -97,7 +97,7 @@ class OperationWriter(object):
 
         imports = set()
         name, args, kwargs = self.operation.deconstruct()
-        argspec = inspect.getargspec(self.operation.__init__)
+        operation_args = get_func_args(self.operation.__init__)
 
         # See if this operation is in django.db.migrations. If it is,
         # We can just use the fact we already have that imported,
@@ -110,15 +110,14 @@ class OperationWriter(object):
 
         self.indent()
 
-        # Start at one because argspec includes "self"
-        for i, arg in enumerate(args, 1):
+        for i, arg in enumerate(args):
             arg_value = arg
-            arg_name = argspec.args[i]
+            arg_name = operation_args[i]
             _write(arg_name, arg_value)
 
         i = len(args)
         # Only iterate over remaining arguments
-        for arg_name in argspec.args[i + 1:]:
+        for arg_name in operation_args[i:]:
             if arg_name in kwargs:  # Don't sort to maintain signature order
                 arg_value = kwargs[arg_name]
                 _write(arg_name, arg_value)
diff --git a/django/db/models/fields/files.py b/django/db/models/fields/files.py
index 3f4c7064e4..aaed449fc6 100644
--- a/django/db/models/fields/files.py
+++ b/django/db/models/fields/files.py
@@ -1,7 +1,6 @@
 import datetime
 import os
 import warnings
-from inspect import getargspec
 
 from django import forms
 from django.core import checks
@@ -13,6 +12,7 @@ from django.db.models.fields import Field
 from django.utils import six
 from django.utils.deprecation import RemovedInDjango20Warning
 from django.utils.encoding import force_str, force_text
+from django.utils.inspect import func_supports_parameter
 from django.utils.translation import ugettext_lazy as _
 
 
@@ -89,8 +89,7 @@ class FieldFile(File):
     def save(self, name, content, save=True):
         name = self.field.generate_filename(self.instance, name)
 
-        args, varargs, varkw, defaults = getargspec(self.storage.save)
-        if 'max_length' in args:
+        if func_supports_parameter(self.storage.save, 'max_length'):
             self.name = self.storage.save(name, content, max_length=self.field.max_length)
         else:
             warnings.warn(
diff --git a/django/db/utils.py b/django/db/utils.py
index 8a27fdc0e2..c6d32a7e9f 100644
--- a/django/db/utils.py
+++ b/django/db/utils.py
@@ -290,8 +290,16 @@ class ConnectionRouter(object):
                 # If the router doesn't have a method, skip to the next one.
                 continue
 
-            argspec = inspect.getargspec(router.allow_migrate)
-            if len(argspec.args) == 3 and not argspec.keywords:
+            if six.PY3:
+                sig = inspect.signature(router.allow_migrate)
+                has_deprecated_signature = not any(
+                    p.kind == inspect.Parameter.VAR_KEYWORD for p in sig.parameters.values()
+                )
+            else:
+                argspec = inspect.getargspec(router.allow_migrate)
+                has_deprecated_signature = len(argspec.args) == 3 and not argspec.keywords
+
+            if has_deprecated_signature:
                 warnings.warn(
                     "The signature of allow_migrate has changed from "
                     "allow_migrate(self, db, model) to "
diff --git a/django/dispatch/dispatcher.py b/django/dispatch/dispatcher.py
index a8181b7ec6..b2d774bda6 100644
--- a/django/dispatch/dispatcher.py
+++ b/django/dispatch/dispatcher.py
@@ -4,6 +4,7 @@ import warnings
 import weakref
 
 from django.utils.deprecation import RemovedInDjango21Warning
+from django.utils.inspect import func_accepts_kwargs
 from django.utils.six.moves import range
 
 if sys.version_info < (3, 4):
@@ -89,24 +90,11 @@ class Signal(object):
 
         # If DEBUG is on, check that we got a good receiver
         if settings.configured and settings.DEBUG:
-            import inspect
             assert callable(receiver), "Signal receivers must be callable."
 
             # Check for **kwargs
-            # Not all callables are inspectable with getargspec, so we'll
-            # try a couple different ways but in the end fall back on assuming
-            # it is -- we don't want to prevent registration of valid but weird
-            # callables.
-            try:
-                argspec = inspect.getargspec(receiver)
-            except TypeError:
-                try:
-                    argspec = inspect.getargspec(receiver.__call__)
-                except (TypeError, AttributeError):
-                    argspec = None
-            if argspec:
-                assert argspec[2] is not None, \
-                    "Signal receivers must accept keyword arguments (**kwargs)."
+            if not func_accepts_kwargs(receiver):
+                raise ValueError("Signal receivers must accept keyword arguments (**kwargs).")
 
         if dispatch_uid:
             lookup_key = (dispatch_uid, _make_id(sender))
diff --git a/django/template/base.py b/django/template/base.py
index deebde7a7c..7f33d79dc7 100644
--- a/django/template/base.py
+++ b/django/template/base.py
@@ -51,10 +51,10 @@ u'<html></html>'
 
 from __future__ import unicode_literals
 
+import inspect
 import logging
 import re
 import warnings
-from inspect import getargspec, getcallargs
 
 from django.template.context import (  # NOQA: imported for backwards compatibility
     BaseContext, Context, ContextPopException, RequestContext,
@@ -66,6 +66,7 @@ from django.utils.encoding import (
 )
 from django.utils.formats import localize
 from django.utils.html import conditional_escape, escape
+from django.utils.inspect import getargspec
 from django.utils.safestring import (
     EscapeData, SafeData, mark_for_escaping, mark_safe,
 )
@@ -723,7 +724,8 @@ class FilterExpression(object):
         plen = len(provided) + 1
         # Check to see if a decorator is providing the real function.
         func = getattr(func, '_decorated_function', func)
-        args, varargs, varkw, defaults = getargspec(func)
+
+        args, _, _, defaults = getargspec(func)
         alen = len(args)
         dlen = len(defaults or [])
         # Not enough OR Too many
@@ -884,7 +886,7 @@ class Variable(object):
                             current = current()
                         except TypeError:
                             try:
-                                getcallargs(current)
+                                inspect.getcallargs(current)
                             except TypeError:  # arguments *were* required
                                 current = context.template.engine.string_if_invalid  # invalid method call
                             else:
diff --git a/django/template/library.py b/django/template/library.py
index 182dacf964..6d8a2fb675 100644
--- a/django/template/library.py
+++ b/django/template/library.py
@@ -1,10 +1,10 @@
 import functools
 import warnings
 from importlib import import_module
-from inspect import getargspec
 
 from django.utils import six
 from django.utils.deprecation import RemovedInDjango21Warning
+from django.utils.inspect import getargspec
 from django.utils.itercompat import is_iterable
 
 from .base import Node, Template, token_kwargs
diff --git a/django/template/loaders/base.py b/django/template/loaders/base.py
index 4c429f7883..dd6b52e2bb 100644
--- a/django/template/loaders/base.py
+++ b/django/template/loaders/base.py
@@ -1,8 +1,8 @@
 import warnings
-from inspect import getargspec
 
 from django.template import Origin, Template, TemplateDoesNotExist
 from django.utils.deprecation import RemovedInDjango21Warning
+from django.utils.inspect import func_supports_parameter
 
 
 class Loader(object):
@@ -28,7 +28,7 @@ class Loader(object):
         args = [template_name]
         # RemovedInDjango21Warning: Add template_dirs for compatibility with
         # old loaders
-        if 'template_dirs' in getargspec(self.get_template_sources)[0]:
+        if func_supports_parameter(self.get_template_sources, 'template_dirs'):
             args.append(template_dirs)
 
         for origin in self.get_template_sources(*args):
diff --git a/django/template/loaders/cached.py b/django/template/loaders/cached.py
index 4c9aa3077b..54146fbfbb 100644
--- a/django/template/loaders/cached.py
+++ b/django/template/loaders/cached.py
@@ -5,11 +5,11 @@ to load templates from them in order, caching the result.
 
 import hashlib
 import warnings
-from inspect import getargspec
 
 from django.template import Origin, Template, TemplateDoesNotExist
 from django.utils.deprecation import RemovedInDjango21Warning
 from django.utils.encoding import force_bytes
+from django.utils.inspect import func_supports_parameter
 
 from .base import Loader as BaseLoader
 
@@ -51,7 +51,7 @@ class Loader(BaseLoader):
             args = [template_name]
             # RemovedInDjango21Warning: Add template_dirs for compatibility
             # with old loaders
-            if 'template_dirs' in getargspec(loader.get_template_sources)[0]:
+            if func_supports_parameter(loader.get_template_sources, 'template_dirs'):
                 args.append(template_dirs)
             for origin in loader.get_template_sources(*args):
                 yield origin
diff --git a/django/utils/deprecation.py b/django/utils/deprecation.py
index a31392abd1..3b8dd1f3a4 100644
--- a/django/utils/deprecation.py
+++ b/django/utils/deprecation.py
@@ -1,3 +1,5 @@
+from __future__ import absolute_import
+
 import inspect
 import warnings
 
diff --git a/django/utils/inspect.py b/django/utils/inspect.py
new file mode 100644
index 0000000000..3e3ad0ac23
--- /dev/null
+++ b/django/utils/inspect.py
@@ -0,0 +1,80 @@
+from __future__ import absolute_import
+
+import inspect
+
+from django.utils import six
+
+
+def getargspec(func):
+    if six.PY2:
+        return inspect.getargspec(func)
+
+    sig = inspect.signature(func)
+    args = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD
+    ]
+    varargs = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.VAR_POSITIONAL
+    ]
+    varargs = varargs[0] if varargs else None
+    varkw = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.VAR_KEYWORD
+    ]
+    varkw = varkw[0] if varkw else None
+    defaults = [
+        p.default for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD and p.default is not p.empty
+    ] or None
+    return args, varargs, varkw, defaults
+
+
+def get_func_args(func):
+    if six.PY2:
+        argspec = inspect.getargspec(func)
+        return argspec.args[1:]  # ignore 'self'
+
+    sig = inspect.signature(func)
+    return [
+        arg_name for arg_name, param in sig.parameters.items()
+        if param.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD
+    ]
+
+
+def func_accepts_kwargs(func):
+    if six.PY2:
+        # Not all callables are inspectable with getargspec, so we'll
+        # try a couple different ways but in the end fall back on assuming
+        # it is -- we don't want to prevent registration of valid but weird
+        # callables.
+        try:
+            argspec = inspect.getargspec(func)
+        except TypeError:
+            try:
+                argspec = inspect.getargspec(func.__call__)
+            except (TypeError, AttributeError):
+                argspec = None
+        return not argspec or argspec[2] is not None
+
+    return any(
+        p for p in inspect.signature(func).parameters.values()
+        if p.kind == p.VAR_KEYWORD
+    )
+
+
+def func_has_no_args(func):
+    args = inspect.getargspec(func)[0] if six.PY2 else [
+        p for p in inspect.signature(func).parameters.values()
+        if p.kind == p.POSITIONAL_OR_KEYWORD and p.default is p.empty
+    ]
+    return len(args) == 1
+
+
+def func_supports_parameter(func, parameter):
+    if six.PY3:
+        return parameter in inspect.signature(func).parameters
+    else:
+        args, varargs, varkw, defaults = inspect.getargspec(func)
+        return parameter in args