Black holes break theories. These sites of extremely large masses in extremely small spaces invoke both of the behemoths of modern physics—general relativity (which rules over large masses) and quantum mechanics (which reigns in small spaces). But the two theories do not get along, and they break down in situations where both apply. For physicists, this is a good thing—it means black holes have revealed a flaw in our existing view of the universe, and offer fertile grounds to look for a solution.
This is one of the best pedagogical articles I've read in SciAm in a long time. Not available online yet, so buy the latest issue of the magazine. The view the YouTube video, click here.