diff --git a/t/integration/tasks.py b/t/integration/tasks.py
index 1aaeed32378..2b4937a3725 100644
--- a/t/integration/tasks.py
+++ b/t/integration/tasks.py
@@ -16,15 +16,18 @@ def identity(x):
 
 
 @shared_task
-def add(x, y):
-    """Add two numbers."""
-    return x + y
+def add(x, y, z=None):
+    """Add two or three numbers."""
+    if z:
+        return x + y + z
+    else:
+        return x + y
 
 
-@shared_task
-def raise_error(*args):
-    """Deliberately raise an error."""
-    raise ValueError("deliberate error")
+@shared_task(typing=False)
+def add_not_typed(x, y):
+    """Add two numbers, but don't check arguments"""
+    return x + y
 
 
 @shared_task(ignore_result=True)
@@ -33,6 +36,12 @@ def add_ignore_result(x, y):
     return x + y
 
 
+@shared_task
+def raise_error(*args):
+    """Deliberately raise an error."""
+    raise ValueError("deliberate error")
+
+
 @shared_task
 def chain_add(x, y):
     (
@@ -162,6 +171,24 @@ def collect_ids(self, res, i):
     return res, (self.request.root_id, self.request.parent_id, i)
 
 
+@shared_task(bind=True, default_retry_delay=1)
+def retry(self, return_value=None):
+    """Task simulating multiple retries.
+
+    When return_value is provided, the task after retries returns
+    the result. Otherwise it fails.
+    """
+    if return_value:
+        attempt = getattr(self, 'attempt', 0)
+        print('attempt', attempt)
+        if attempt >= 3:
+            delattr(self, 'attempt')
+            return return_value
+        self.attempt = attempt + 1
+
+    raise self.retry(exc=ExpectedException(), countdown=5)
+
+
 @shared_task(bind=True, expires=60.0, max_retries=1)
 def retry_once(self, *args, expires=60.0, max_retries=1, countdown=0.1):
     """Task that fails and is retried. Returns the number of retries."""
diff --git a/t/integration/test_tasks.py b/t/integration/test_tasks.py
index edfda576f5b..ca71196a283 100644
--- a/t/integration/test_tasks.py
+++ b/t/integration/test_tasks.py
@@ -1,10 +1,14 @@
+from datetime import datetime, timedelta
+from time import sleep, perf_counter
+
 import pytest
 
+import celery
 from celery import group
 
 from .conftest import get_active_redis_channels
-from .tasks import (ClassBasedAutoRetryTask, add, add_ignore_result,
-                    print_unicode, retry_once, retry_once_priority, sleeping)
+from .tasks import (ClassBasedAutoRetryTask, add, add_ignore_result, add_not_typed, retry,
+                    print_unicode, retry_once, retry_once_priority, sleeping, fail, ExpectedException)
 
 TIMEOUT = 10
 
@@ -28,8 +32,200 @@ def test_class_based_task_retried(self, celery_session_app,
         assert res.get(timeout=TIMEOUT) == 1
 
 
+def _producer(j):
+    """Single producer helper function"""
+    results = []
+    for i in range(20):
+        results.append([i + j, add.delay(i, j)])
+    for expected, result in results:
+        value = result.get(timeout=10)
+        assert value == expected
+        assert result.status == 'SUCCESS'
+        assert result.ready() is True
+        assert result.successful() is True
+    return j
+
+
 class test_tasks:
 
+    def test_simple_call(self):
+        """Tests direct simple call of task"""
+        assert add(1, 1) == 2
+        assert add(1, 1, z=1) == 3
+
+    @flaky
+    def test_basic_task(self, manager):
+        """Tests basic task call"""
+        results = []
+        # Tests calling task only with args
+        for i in range(10):
+            results.append([i + i, add.delay(i, i)])
+        for expected, result in results:
+            value = result.get(timeout=10)
+            assert value == expected
+            assert result.status == 'SUCCESS'
+            assert result.ready() is True
+            assert result.successful() is True
+
+        results = []
+        # Tests calling task with args and kwargs
+        for i in range(10):
+            results.append([3*i, add.delay(i, i, z=i)])
+        for expected, result in results:
+            value = result.get(timeout=10)
+            assert value == expected
+            assert result.status == 'SUCCESS'
+            assert result.ready() is True
+            assert result.successful() is True
+
+    @flaky
+    def test_multiprocess_producer(self, manager):
+        """Testing multiple processes calling tasks."""
+        from multiprocessing import Pool
+        pool = Pool(20)
+        ret = pool.map(_producer, range(120))
+        assert list(ret) == list(range(120))
+
+    @flaky
+    def test_multithread_producer(self, manager):
+        """Testing multiple threads calling tasks."""
+        from multiprocessing.pool import ThreadPool
+        pool = ThreadPool(20)
+        ret = pool.map(_producer, range(120))
+        assert list(ret) == list(range(120))
+
+    @flaky
+    def test_ignore_result(self, manager):
+        """Testing calling task with ignoring results."""
+        result = add.apply_async((1, 2), ignore_result=True)
+        assert result.get() is None
+
+    @flaky
+    def test_timeout(self, manager):
+        """Testing timeout of getting results from tasks."""
+        result = sleeping.delay(10)
+        with pytest.raises(celery.exceptions.TimeoutError):
+            result.get(timeout=5)
+
+    @flaky
+    def test_expired(self, manager):
+        """Testing expiration of task."""
+        # Fill the queue with tasks which took > 1 sec to process
+        for _ in range(4):
+            sleeping.delay(2)
+        # Execute task with expiration = 1 sec
+        result = add.apply_async((1, 1), expires=1)
+        with pytest.raises(celery.exceptions.TaskRevokedError):
+            result.get()
+        assert result.status == 'REVOKED'
+        assert result.ready() is True
+        assert result.failed() is False
+        assert result.successful() is False
+
+        # Fill the queue with tasks which took > 1 sec to process
+        for _ in range(4):
+            sleeping.delay(2)
+        # Execute task with expiration at now + 1 sec
+        result = add.apply_async((1, 1), expires=datetime.utcnow() + timedelta(seconds=1))
+        with pytest.raises(celery.exceptions.TaskRevokedError):
+            result.get()
+        assert result.status == 'REVOKED'
+        assert result.ready() is True
+        assert result.failed() is False
+        assert result.successful() is False
+
+    @flaky
+    def test_eta(self, manager):
+        """Tests tasks scheduled at some point in future."""
+        start = perf_counter()
+        # Schedule task to be executed in 3 seconds
+        result = add.apply_async((1, 1), countdown=3)
+        sleep(1)
+        assert result.status == 'PENDING'
+        assert result.ready() is False
+        assert result.get() == 2
+        end = perf_counter()
+        assert result.status == 'SUCCESS'
+        assert result.ready() is True
+        # Difference between calling the task and result must be bigger than 3 secs
+        assert (end - start) > 3
+
+        start = perf_counter()
+        # Schedule task to be executed at time now + 3 seconds
+        result = add.apply_async((2, 2), eta=datetime.utcnow() + timedelta(seconds=3))
+        sleep(1)
+        assert result.status == 'PENDING'
+        assert result.ready() is False
+        assert result.get() == 4
+        end = perf_counter()
+        assert result.status == 'SUCCESS'
+        assert result.ready() is True
+        # Difference between calling the task and result must be bigger than 3 secs
+        assert (end - start) > 3
+
+    @flaky
+    def test_fail(self, manager):
+        """Tests that the failing task propagates back correct exception."""
+        result = fail.delay()
+        with pytest.raises(ExpectedException):
+            result.get(timeout=5)
+        assert result.status == 'FAILURE'
+        assert result.ready() is True
+        assert result.failed() is True
+        assert result.successful() is False
+
+    @flaky
+    def test_wrong_arguments(self, manager):
+        """Tests that proper exceptions are raised when task is called with wrong arguments."""
+        with pytest.raises(TypeError):
+            add(5)
+
+        with pytest.raises(TypeError):
+            add(5, 5, wrong_arg=5)
+
+        with pytest.raises(TypeError):
+            add.delay(5)
+
+        with pytest.raises(TypeError):
+            add.delay(5, wrong_arg=5)
+
+        # Tasks with typing=False are not checked but execution should fail
+        result = add_not_typed.delay(5)
+        with pytest.raises(TypeError):
+            result.get(timeout=5)
+        assert result.status == 'FAILURE'
+
+        result = add_not_typed.delay(5, wrong_arg=5)
+        with pytest.raises(TypeError):
+            result.get(timeout=5)
+        assert result.status == 'FAILURE'
+
+    @flaky
+    def test_retry(self, manager):
+        """Tests retrying of task."""
+        # Tests when max. retries is reached
+        result = retry.delay()
+        for _ in range(5):
+            status = result.status
+            if status != 'PENDING':
+                break
+            sleep(1)
+        assert status == 'RETRY'
+        with pytest.raises(ExpectedException):
+            result.get()
+        assert result.status == 'FAILURE'
+
+        # Tests when task is retried but after returns correct result
+        result = retry.delay(return_value='bar')
+        for _ in range(5):
+            status = result.status
+            if status != 'PENDING':
+                break
+            sleep(1)
+        assert status == 'RETRY'
+        assert result.get() == 'bar'
+        assert result.status == 'SUCCESS'
+
     @flaky
     def test_task_accepted(self, manager, sleep=1):
         r1 = sleeping.delay(sleep)