Black hole coalescence and mergers: Review, status, and "Where are we heading?"

I review recent progress in 3D numerical relativity, focusing on simulations involving black holes evolved with singularity avoiding slicings. After a long series of axisymmetric and perturbative studies of distorted black holes and black hole collisions, similar studies were carried out with full 3D codes. The results show that such black hole simulations can be carried out extremely accurately, although instabilities plague the simulation at uncomfortably early times. However, new formulations of Einstein's equations allow much more stable 3D evolutions than ever before, enabling the first studies of 3D gravitational collapse to a black hole. With these new formulations, for example, it has become possible to perform the first detailed simulations of 3D grazing collisions of black holes with unequal mass and spin, and with orbital angular momentum. I discuss the 3D black hole physics that can now be studied, and prospects for the future. Such studies may be able to provide information about the final plunge of two black holes, which is relevant to gravitational wave astronomy, and will be very useful as a foundation for future studies when advanced techniques like black hole excision mature to the point that they permit full orbital coalescence simulations.