Abstract: The radiation from stellar-size black holes spiraling in to much larger black holes in the centers of galaxies and (perhaps) globular clusters can be computed in black-hole perturbation theory, with the smaller black hole modeled as a point particle. To extract the physical properties of the system from the observed waveform one needs to compute the self-force of the small black hole, a calculation that involves renormalizing the field at the particle. Adopting a radiation gauge allows one to use the decoupled, separable Teukolsky equation, but several obstacles needed to be overcome before the first successful computations were completed. The successes now include the first computation of the change in the angular velocity of orbits in a Kerr geometry (a near gauge-invariant) and a computation of the self-force for circular orbits in a Schwarzschild background. Extending the self-force calculation to Kerr is now underway.