Astrophysical fluids underlie almost every astrophysical process in the Universe, from the formation of stars and planets on small scales to the formation and evolution of cosmic structures on the largest. The numerical tools used to solve for the evolution of astrophysical fluids share much in common, bringing together diverse astrophysical topics under a common set of methods. The two principal techniques for solving the fluid equations are finite difference methods and Smoothed Particle Hydrodynamics (SPH). (For a comparison of the two methods in the context of astrophysical applications, see here .) Areas of particular interest are structure formation after the Big Bang, particularly the Intergalactic Medium and clusters of galaxies, the formation and evolution of galaxies and black holes, the formation of stars and their associated planetary systems, and the merger of compact objects like neutron stars and black holes leading to the production of gamma-ray bursts.