Aquatic animals propel themselves using a wide variety of mechanisms. In fish, eels, dolphins and manta rays, propulsion is achieved by combining oscillating and undulatory motions of flexible surfaces. We are interested in studying the unsteady hydrodynamics of such motions to understand and model the wake structure. Experiments have been conducted on flapping flexible membranes, flapping rigid plates, and mechanical models of eels and manta rays. Preliminary observations suggest a rich set of phenomena exist, depending on the non-dimensional frequency of flapping and the aspect ratio of the foil. Under certain conditions, simple wake structures are observed that bear a strong resemblance to the structure of co-flowing jets and wakes.