2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36159We summarize the state of the art of the ``close approximation'' to black hole collisions. We discuss results to first and second order in perturbation theory for head-on collisions of momentarily-stationary and non-stationary black holes and discuss the near-future prospect of non-axisymmetric collisions.19 pages, crckapb.sty, 7 figures included with psfig, talk given at GR15, Poona, India, to appear in the proceedingsGeneral Relativity and Quantum Cosmologytext