Simulations of the structure and dynamics of fluid films confined to a thickness of a few molecular diameters are described. Confining walls introduce layering and in-plane order in the adjacent fluid. The latter is essential to transfer of shear stress. As the film thickness is decreased, by increasing pressure or decreasing the number of molecular layers, the entire film may undergo a phase transition. Spherical molecules tend to crystallize, while short chain molecules enter a glassy state with strong local orientational and translational order. These phase transitions lead to dramatic changes in the response of the film to imposed shear velocities v. Spherical molecules show an abrupt transition from Newtonian response to a yield stress as they crystallize. Chain molecules exhibit a continuously growing regime of non-Newtonian behavior where the shear viscosity drops as v −2/3 at constant normal load. The same power law is found for a wide range of parameters, and extends to lower and lower velocities as a glass transition is approached. Once in the glassy state, 1 chain molecules exhibit a finite yield stress. Shear may occur either within the film or at the film/wall interface. Interfacial shear dominates when films become glassy and when the film viscosity is increased by increasing the chain length.