"Merging of neutron star binaries in full general relativity": The merger of a binary system of compact objects is expected to be a strong source of gravitational waves, but will also be accompanied by an intense electromagnetic signature. I will overview the rapid recent progress in this problem and show how the dynamics of a binary of magnetized neutron stars leads to a rapidly-spinning black hole surrounded by a hot and highly-magnetized torus. I will also discuss how this process can be used to model short gamma-ray bursts and infer the properties of the equation of state for matter at nuclear densities.