Fair use?

I just read about this over on Chemistry Central. Basically, a graduate student blogger at the University of Michigan was threatened with legal action for using some copyrighted figures in her blog. Fortunately the matter has been resolved, but it still opens up the question: What is fair use?

Anyway, I'd almost prefer an email like that over this kind of unpleasantness. I guess I'm lucky that my boss is a nice guy.