During contact metamorphism, fluid production from magma and wall rocks, thermal expansion of fluid, thermal and chemical buoyancy, topography, and deformation of rocks all interact to drive fluid flow. An understanding of how these processes interact is necessary to predict the evolution of fluid flow, fluid pressures, and permeability; to evaluate mechanisms of ore deposition, metasomatism, and heat transfer; and to apply petrologic, field, and geochemical data to infer hydrologic histories. Results from finite-difference models that account for many of these processes reveal the hydrodynamics of contact metamorphism. A systematic evolution in flow system from lithostatic fluid pressures and expulsion of internally generated fluids, to hydrostatic fluid pressures and circulation of externally derived fluids is predicted to occur with time, increasing permeability, and decreasing depth. Fluid production from magmas and wall rocks is the dominant process elevating fluid pressures toward lithostatic values during prograde metamorphism; other processes, such as strain or thermal expansion of the fluid, are less significant. For typical water contents of magmas and wall rocks, permeabilities of ≤1 μd (10−18 m2) are required to produce lithostatic fluid pressures in the aureole. Consideration of processes controlling permeability suggests that fluid flow is likely intergranular during prograde metamorphism and channelized during retrograde metamorphism. Balance of rates of thermal fracturing and mineral deposition implies that permeability should increase above 1 μd during cooling, and thus fluid pressures should drop abruptly toward hydrostatic values once cooling and fracturing ensues. Rocks near the contact cool first, and complex mixing of magmatic, metamorphic, and meteoric fluids is likely in this region. If permeability increases during cooling, meteoric fluids may dominate the total fluid budget even though rocks interact with only magmatic and metamorphic fluids during prograde metamorphism. Many broad features of the models are similar to patterns observed in porphyry copper deposits. Models with ad hoc assumptions of permeability near the contact are required to produce significant up-temperature fluid flow during prograde metamorphism, a pattern predicted from some reaction-transport models.