Numerical simulations with supercomputers allow analysis of the wide range of nonlinear physics inherent in the hydrodynamic and magnetohydrodynamic equations. When applied to extragalactic radio sources, these numerical models have begun to reproduce many of the complex structures observed on telescopic images. This combination of telescopic and numerical observations provides powerful probes of the physics of radio galaxies. In this review, some of the recent results from both two-dimensional and three-dimensional numerical simulations of the formation and evolution of extended radio morphologies are described. These numerical models have allowed the exploration of important physical phenomena including the role of magnetic fields in the dynamics and emissivity of extended radio galaxies, intermittent outflow from the cores of active galaxies, instabilities and disruption of fluid jets, and the bending of collimated outflows by motion through the intergalactic medium.