  We review the current status of attempts to numerically model the merger of
neutron star-neutron star (NSNS) and black hole-neutron star (BHNS) binary
systems, and we describe the understanding of such events that is emerging from
these calculations. To accurately model the physics of NSNS and BHNS mergers is
a difficult task. It requires solving Einstein's equations for dynamic
spacetimes containing black holes. It also requires evolving the hot,
supernuclear-density neutron star matter together with the magnetic and
radiation fields that can influence the post-merger dynamics. Older studies
concentrated on either one or the other of these challenges, but now efforts
are being made to model both relativity and microphysics accurately together.
These NSNS and BHNS simulations are then used to characterize the gravitational
wave signals of such events and to address their potential for generating
short-duration gamma ray bursts.
