A simple problem in Newtonian gravity, the motion of two bodies about one another is far more challenging in general relativity.  Motivated largely by the anticipated importance of compact binaries as gravitational-wave sources, many years of effort have produced a suite of tools for modeling binaries in general relativity.  This work has culminated in the celebrated recent breakthroughs in numerical relativity allowing us to model essentially arbitrary compact binary systems.  In this talk, I will present an overview of what we have learned from GR's two-body problem, focusing in particular on how unique aspects of general relativity flavor the gravitational waves which binaries generate.  I will also describe how measuring these waves and exploiting these models will allow us to study compact bodies, especially black holes, in exquisite detail.

Scott Hughes