Abstract: The talk will be divided into two parts. In the first part, I will describe the difficulties that for many decades plagued simulations of black hole spacetimes as well as the techniques that have been developed to overcome them. I will attempt to give an (in no way comprehensive) overview of the astrophysical results coming from simulations of binary black hole systems. In the second part I will switch gears and describe recently developed multipatch techniques that we are now attempting to apply to the problem of the self force calculation of a scalar charge in orbit around a black hole.