If space in the universe is expanding, then why is the Andromeda galaxy on a collision course with ours?

I have watched enough specials on PBS and the Science channel to know that the universe is expanding and that everything is supposedly moving away from everything else in the universe. However, this does not jive with the reported fact that our nearest neighboring galaxy (Andromeda) is on a collision course with our own galaxy (the Milky Way) and that galactic collisions are commonplace throughout the observable universe. How do astronomers maintain the expanding universe model in the face of this evidence?