Most of the visible matter in the Universe is a plasma, that is a dilute gas of electrons, ions, and neutral particles. In many cases the dynamics of this plasma is described to a good approximation by the equations of compressible hydrodynamics, magneto-hydrodynamics (in the case that magnetic fields are present), or radiation MHD (in the case that photons provide significant energy or momentum transport). Studying multidimensional, time-dependent and/or highly nonlinear processes in astrophysical plasmas usually requires numerical methods, however developing accurate and robust methods for compressible MHD and/or radiation MHD is still an active area of research in applied mathematics. I will describe some problems in astrophysics which motivate the development of such methods, describe recent advance in numerical algorithms for MHD and their implementation on parallel processors, and describe some of what we have learned from application of the methods. References: Gardiner & Stone, JCP, 205, 509 (2005) LeVeque, Finite Volume Methods for Hyperbolic Conservation Laws