Abstract: Galactic nuclei are the sites of a number of unique physical phenomena, due to their high densities and the presence of supermassive black holes. Among the novel observational signatures that might be detected from galactic nuclei in the near future are gravitational waves from coalescing black holes and WIMP annihilations from regions of high dark matter density. Predicting the rates of such events and interpreting the signals will require a better understanding of the dynamical interaction between black holes, stars, and dark matter. I discuss recent work on this topic, including results from a new generation of special-purpose supercomputers.