Gravitational waves from inspiral into massive black holes

Space-based gravitational-wave interferometers such as LISA will be sensitive to the inspiral of stellar mass compact objects into black holes with masses in the range of roughly 10^5 solar masses to (a few) 10^7 solar masses. During the last year of inspiral, the compact body spends several hundred thousand orbits spiraling from several Schwarzschild radii to the last stable orbit. The gravitational waves emitted from these orbits probe the strong-field region of the black hole spacetime and can make possible high precision tests and measurements of the black hole's properties. Measuring such waves will require a good theoretical understanding of the waves' properties, which in turn requires a good understanding of strong-field radiation reaction and of properties of the black hole's astrophysical environment which could complicate waveform generation. In these proceedings, I review estimates of the rate at which such inspirals occur in the universe, and discuss what is being done and what must be done further in order to calculate the inspiral waveform.