Today we have a solid theoretical understanding of the dynamics of black holes, as predicted by general relativity, for the typical binary merger expected as an astrophysical gravitational wave source. However, in more "extreme" situations, namely black holes that collide with ultrarelativistic velocities, and black holes that spin near the maximal limit allowed by general relativity, less is known, in some cases even qualitatively. In this talk I will discuss some of these open problems, and speculate about possible answers.