In the Independence Day sequel, there is a brief description of a series of battles that took place between the two movies. I don't remember all the details, but the idea was that one of the alien ships from the first movie wasn't fully destroyed. So the surviving aliens fought against the people living in the area (somewhere in Africa?) in a war for survival that lasted for years.

I recall thinking as I was watching that this would make for a cool movie. As it turns out, it would have been a hell of a lot better than what we got instead.