As of 2.7 (per the documentation) you get setUpClass and tearDownClass which execute before and after the tests in a given class are run, respectively. Alternatively, if you have a group of them in one file, you can use setUpModule and tearDownModule (documentation).

EDIT: Note that setUpClass and tearDownClass must be declared using @classmethod. Another answer to this question includes sample code.

Otherwise your best bet is probably going to be to create your own derived TestSuite and override run(). All other calls would be handled by the parent, and run would call your setup and teardown code around a call up to the parent's run method.

You can use setUp()(docs) and setUpClass()(docs) methods for this. The setUp() method is executed before each individual test while the setUpClass() method is executed before all the tests in this class run.

import unittest

class MyTests(unittest.TestCase):

    @classmethod
    def setUpClass(cls):
        print("Starting all the tests.")

    def setUp(self):
        print("Starting another test.")

    def test_first(self):
        ...

The problem was that in those 2 answers, the startTestRun method was not in any class. It should be like this:

import unittest

class TestResult(object):
    def startTestRun(self):
        print('once before all tests')


setattr(unittest.TestResult, 'startTestRun', TestResult.startTestRun)

If you need to tidy up after all tests, that's the same with stopTestRun:

import unittest

class TestResult(object):
    def stopTestRun(self):
        print('once after all tests')


setattr(unittest.TestResult, 'stopTestRun', TestResult.stopTestRun)

Assuming that you're properly using a class descended from unittest.TestCase, then the setUp method is run before each test, and the tearDown method is run after each test. Check the documentation. So it's completely feasible to put your code in those two methods.