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We review the current status of attempts to numerically model the merger ofneutron star-neutron star (NSNS) and black hole-neutron star (BHNS) binarysystems, and we describe the understanding of such events that is emerging fromthese calculations. To accurately model the physics of NSNS and BHNS mergers isa difficult task. It requires solving Einstein's equations for dynamicspacetimes containing black holes. It also requires evolving the hot,supernuclear-density neutron star matter together with the magnetic andradiation fields that can influence the post-merger dynamics. Older studiesconcentrated on either one or the other of these challenges, but now effortsare being made to model both relativity and microphysics accurately together.These NSNS and BHNS simulations are then used to characterize the gravitationalwave signals of such events and to address their potential for generatingshort-duration gamma ray bursts.

Numerical relativity confronts compact neutron star binaries: a review and status report