From one point of view, the ocean is a vast and complicated dynamical system. Its circulation of water is made up of fluid particle trajectories whose chaotic motion accounts for significant exchange of fluid between regions of ostensibly different types of motion. This is particularly evident around large coherent features, such as ocean eddies (which are the ocean’s version of hurricanes) and major currents, such as the Gulf Stream. The modern theory of dynamical systems has shed considerable light on these processes. It will also be shown how they promise improved strategies for data gathering and analysis.