It has been known since the work of Madelung in the 1920s that there is a hydrodynamic interpretation of quantum mechanics in which the Schrödinger equation is expressed in terms of a continuity equation and an Euler equation involving a so-called “quantum potential.” This idea was revived by Widrow & Kaiser (1992) but in reverse, using wave mechanics to represent a fluid flow. I this talk I outline the basics of this Schrödinger equation, its relation to the Hamilton-Jacobi formalism, and some advantages it offers over traditional perturbative approaches to the nonlinear evolution of self-gravitating fluids. I illustrate some of these advantages using a range of examples, particularly cases of dynamical reconstruction of density fields.