  This paper reviews the basic features of the theory of curvature
perturbations in Kerr spacetime, which is customarily written in terms of gauge
invariant components of the Weyl tensor which satisfy a perturbation equation
known as the Teukolsky equation. I will describe how to evolve generic
perturbations about the Kerr metric and the separable form of the wave
solutions that one obtains, and the relation of the Teukolsky function to the
energy of gravitational waves emitted by the black hole. A discussion of a
numerical scheme to evolve perturbations as a function of time and some
preliminary results of our research project implementing it for matter sources
falling into the black hole is included.
