  In this review article I attempt to summarise past and present-ongoing-work
on the problem of the inspiral of a small body in the gravitational field of a
much more massive Kerr black hole. Such extreme mass ratio systems, expected to
occur in galactic nuclei, will constitute prime sources of gravitational
radiation for the future LISA gravitational radiation detector. The article's
main goal is to provide a survey of basic celestial mechanics in Kerr spacetime
and calculations of gravitational waveforms and backreaction on the small
body's orbital motion, based on the traditional `flux-balance' method and the
Teukolsky black hole perturbation formalism.
