  The computation of gravitational radiation generated by the coalescence of
inspiralling binary black holes is nowdays one of the main goals of numerical
relativity. Perturbation theory has emerged as an ubiquitous tool for all those
dynamical evolutions where the two black holes start close enough to each
other, to be treated as single distorted black hole (close limit
approximation), providing at the same time useful benchmarks for full numerical
simulations. Here we summarize the most recent developments to study evolutions
of perturbations around rotating (Kerr) black holes. The final aim is to
generalize the close limit approximation to the most general case of two
rotating black holes in orbit around each other, and thus provide reliable
templates for the gravitational waveforms in this regime. For this reason it
has become very important to know if these predictions can actually be trusted
to larger separation parameters (even in the region where the holes have
distinct event horizons). The only way to extend the range of validity of the
linear approximation is to develop the theory of second order perturbations
around a Kerr hole, by generalizing the Teukolsky formalism.
