Black hole-neutron star mergers likely produce strong gravitational wave, neutrino, and electromagnetic signals which together provide a wealth of information about the binary and about the hyperaccreting black hole system produced by its merger. In this talk, I describe efforts by the SXS collaboration to model these violent events by numerically evolving the spacetime and nuclear matter. This task is divided into two parts. First, we explore the large black hole-neutron star parameter space using simplified microphysics. Second, we study what we take to be the most representative cases using nuclear theory-based equations of state and approximate neutrino radiation. Finally, I discuss remaining problems to be solved for simulations investigating a merger/gamma-ray burst connection.