A wave-powered water vehicle includes a surface float, a submerged swimmer, and a tether which connects the float and the swimmer, so that the swimmer moves up and down as a result of wave motion. The swimmer includes one or more fins which interact with the water as the swimmer moves up and down, and generate forces which propel the vehicle forward. The vehicle, which need not be manned, can carry communication and control equipment so that it can follow a course directed by signals sent to it, and so that it can record or transmit data from sensors on the vehicle.