  We describe progress evolving an important limit of binary orbits in general
relativity, that of a stellar mass compact object gradually spiraling into a
much larger, massive black hole. These systems are of great interest for
gravitational wave observations. We have developed tools to compute for the
first time the radiated fluxes of energy and angular momentum, as well as
instantaneous snapshot waveforms, for generic geodesic orbits. For special
classes of orbits, we compute the orbital evolution and waveforms for the
complete inspiral by imposing global conservation of energy and angular
momentum. For fully generic orbits, inspirals and waveforms can be obtained by
augmenting our approach with a prescription for the self force in the adiabatic
limit derived by Mino. The resulting waveforms should be sufficiently accurate
to be used in future gravitational-wave searches.
