The field of astrophysical fluid dynamics (AFD) is described as an emerging discipline which derives historically from both the theory of stellar evolution and space plasma physics. The fundamental physical assumption behind AFD is that fluid equations of motion accurately describe the evolution of plasmas on scales that are large in comparison with particle interaction length scales. Particular attention is given to purely fluid models of large-scale astrophysical plasmas. The role of computer simulation in AFD research is also highlighted and a suite of general-purpose application codes for AFD research is discussed. The codes are called ZEUS-2D and ZEUS-3D and solve the equations of AFD in two and three dimensions, respectively, in several coordinate geometries for general initial and boundary conditions. The topics of bipolar outflows from protostars, galactic superbubbles and supershells, and extragalactic radio sources are addressed.