We are on the verge of a truly remarkable observational possibility: the direct detection of black holes, or at least as direct as is theoretically possible. We won't use our eyes, telescopes, or any other detector of electromagnetic radiation. Instead, we hope to be able to observe black holes through gravitational waves. Yet the dynamics of realistic, astrophysical black hole pairs is surprisingly not well understood, difficult to solve, and possibly even chaotic. I will discuss a dynamical systems approach to studying the full range of orbits available to black hole pairs, including chaotic orbits. An understanding of the dynamics is crucial to the future success of gravitational wave observatories. In the meantime, regions of interesting dynamics could be identified and fed into the new and powerful simulations of numerical relativity for more detailed studies.