The goal of this book is to show how potential flows enter into the general theory of motions of viscous and viscoelastic fluids. Traditionally, the theory of potential flows is thought to apply to idealized fluids without viscosity. Here we show how to apply this theory to real fluids that are viscous. The theory is applied to problems of the motion of bubbles; to the decay of waves on interfaces between fluids; to capillary, Rayleigh-Taylor, and Kelvin-Hemholtz instabilities; to viscous effects in acoustics; to boundary layers on solids at finite Reynolds numbers; to problems of stress-induced cavitation; and to the creation of microstructures in the flow of viscous and viscoelastic liquids.