There are over 28,000 species of fishes, and a key feature of this remarkable evolutionary diversity is a great variety of propulsive systems used by fishes for maneuvering in the aquatic environment. Fishes have numerous control surfaces (fins) which act to transfer momentum to the surrounding fluid. Most fishes are unstable and use several control surfaces simultaneously for propulsion and to maintain body position. In this presentation I will discuss the results of recent experimental kinematic and hydrodynamic studies of fish fin function, and their implications for the construction of robotic models of fishes. Recent high-resolution video analyses of fish fin movements during locomotion show that fins undergo much greater deformations than previously suspected. Experimental work on fin mechanics shows that fishes possess a mechanism for actively adjusting fin surface curvature to modulate locomotor force. Fish fin motion results in the formation of vortex rings of various conformations, and quantification of vortex rings shed into the wake by freely-swimming fishes has proven to be useful for understanding the mechanisms of propulsion. Experimental analyses of propulsion in freely-swimming fishes have lead to the development of three self-propelling robotic models: a pectoral fin robotic device, a robotic fish tail, and a flapping flexible foil robotic model of fish body deformation; I will discuss the design of each robotic model along with recent results and their implications for understanding the biomechanics of underwater propulsion.