I know about cutting a line on the concave side to loosen it, and then gluing in strips of wood once flat, and I know of using water on one side and then laying things on top to help it dry flat. Are there any other ways of making warped wood flat again?
Common wisdom is that if you have access to a jointer and planer, you will joint the board on the cupped side to flatten it, then use the planer to produce a smooth edge on the opposite side. If you don't have a jointer, there are some jigs available that can attempt to replicate a jointer's function on just a planer. If you don't have a planer, well, you'll be stuck using a hand plane to shave the warped portions off.
One thing I failed to mention is that one can also use a router to flatten a board; it seems a bit like a kludge but I wager many people have used this technique in absence of a jointer or planer. The Wood Whisperer has a good video about this: TWW 174 on YouTube