When two neutron stars in a binary collide, they merge into a massive object which most likely collapses to a black hole. If, after the collapse, a significant amount of matter remains outside the hole in orbit around it, the system could drive a burst of gamma ray emission which could be detected on Earth. (Indeed, we may have already detected gamma ray bursts associated with such events.) In order to study the post-merger evolution of binary neutron star systems, it is necessary to carry out numerical simulations using the equations of general relativistic magnetohydrodynamics. In this talk, I will describe the first such calculations. I will also discuss the challenges involved in evolving spacetimes in general relativity. Extensive prior knowledge in astrophysics should not be required to follow this talk.