Title: Black hole-neutron star binaries

Abstract: The gravitational wave signals of black hole-neutron star (BHNS) binary systems have now been detected, and future detections might be accompanied by electromagnetic counterparts. BHNS mergers involve much of the same physics as binary neutron star mergers: strong gravity, nuclear density matter, neutrino radiation, and magnetic turbulence. They also share with binary neutron star systems the potential for bright electromagnetic signals, especially gamma ray bursts and kilonovae, and the potential to be significant sources of r-process elements. However, BHNS binaries are more asymmetric, and their mergers produce different amounts and arrangements of the various post-merger material components (e.g. disk and dynamical ejecta), together with a more massive black hole; these differences can have interesting consequences. In this chapter, we review the modeling of BHNS mergers and post-merger evolution in numerical relativistic hydrodynamics and magnetohydrodynamics. We attempt to give readers a broad understanding of the answers to the following questions. What are the main considerations that determine the merger outcome? What input physics must (or should) go into a BHNS simulation? What have the most advanced simulations to date learned?