Encounters between stars and stellar remnants at the centers of galaxies drive many important processes, including generation of gravitational waves via extreme-mass-ratio inspirals (EMRIs). The fact that these encounters take place near a supermassive black hole (SMBH) turns out to be important for two reasons: (1) The orbital motion is quasi-Keplerian, so that correlations are maintained for much longer than in purely random encounters. (2) Relativity affects the motion, through mechanisms like precession of the periapse and frame-dragging. The interplay between these processes is just now beginning to be understood, based on N-body simulations that contain a post-Newtonian representation of relativistic dynamics. A key result is that relativity can be important even for orbits that extend outward to a substantial fraction of the SMBH influence radius, by destroying the long-term correlations that would otherwise drive the evolution. I will discuss this work and its implications for the EMRI problem, for experimental tests of theories of gravity, and for the long-term evolution of SMBHs and galactic nuclei.