In this paper, we present a method for fluid simulation on arbitrary quadrilateral surface meshes. We solve the Navier-Stokes equations by performing the traditional steps of fluid simulation, semi-Lagrangian advection and pressure projection, directly on the surface. We include level-set based front-tracking for visualizing "liquids", while we use densities to visualize "smoke". We demonstrate our method on a variety of meshes and create an assortment of visual effects.