Supercomputer simulations have been used in conjunction with analytic studies to investigate the central issue of astrophysical accretion-disk dynamics : the nature of the angular momentum transport. Simulations provide the means to investigate and experiment with candidate mechanisms, including global hydrodynamic instabilities, spiral shock waves, and local magnetohydrodynamic (MHD) instabilities. Simulations have demonstrated that accretion disks are generally MHD turbulent. These results suggest that the fundamental physical mechanism for angular momentum transport in accretion disks has now been identified.