We've heard all the brouhaha surrounding the bumble bee ability to fly in spite of the (erroneous) claim that physics says that it can't. This is false of course because the "physics" being used is based on a fixed-wing scenario.
In any case, it doesn't mean other flying creatures should be ignored! This is an informative and in-depth article on the physics of a dragonfly flight. There's even an avi video that you can view (scroll to the bottom of the article) showing a high-speed video of how the wings of a dragonfly move.
A fun article to read if you're bored.