The focus of this proposal for a 5-day multidisciplinary workshop at the Banff International Research Station is the mathematics of free-surface fluid flow. Building on striking theoretical and experimental developments of the last few years, the workshop will bring together mathematicians and physicists at the forefront of research in experiments, analysis, computation, and modeling. The workshop promises a rich exchange of ideas in the areas of thin liquid films, dynamic contact lines, slender jets, Hele-Shaw flow and fluid interfaces.