The damped wave equation is a prototype of a non-selfadjoint PDE, which means that the stationary problem has complex spectrum.  The asymptotic distribution of the spectrum is heavily influenced by properties of the geodesic flow, and in part determines the rate of decay to equilibrium.  In this talk, I will survey recent results on such decay estimates for the damped and over-damped wave equation, followed by a description of work-in-progress applying damped wave methods to systems arriving in the analysis of certain microfluidic mixing devices.