In the lubrication approximation, the motion of a thin liquid film is described by a single fourth-order partial differential equation that models the evolution of the height of the film. When the fluid is driven by a Marangoni force generated by a distribution of insoluble surfactant, the thin film equation is coupled to an equation for the concentration of surfactant. In this talk, I show the basic structure of this system, and begin an analysis of wave-like solutions in the specific context of a thin film flowing down an inclined plane. Numerical simulations reveal an array of traveling waves, which persists when capillarity and surface diffusion are neglected. The analysis of the limiting system has some surprises, and in this talk, I show how far we have come in understanding the numerical results analytically, and the analytical results numerically.