Most of the kinetic energy of ocean circulation is contained in ubiquitous mesoscale eddies. Their prominent signatures in sea surface height have rendered satellite altimetry highly effective in observing global ocean eddies. Our knowledge of ocean eddy dynamics has grown by leaps and bounds since the advent of satellite altimetry in the early 1980s. A satellite's fast sampling allows a broad view of the global distribution of eddy variability and its spatial structures. Since the early 1990s, the combination of data available from two simultaneous flying altimeters has resulted in a time-series record of global maps of ocean eddies. Despite the moderate resolution, these maps provide an opportunity to study the temporal and spatial variability of the surface signatures of eddies at a level of detail previously unavailable. A global census of eddies has been constructed to assess their population, polarity, intensity, and nonlinearity. The velocity and pattern of eddy propagation, as well as eddy transports of heat and salt, have been mapped globally. For the first time, the cascade of eddy energy through various scales has been computed from observations, providing evidence for the theory of ocean turbulence. Notwithstanding the tremendous progress made using existing observations, their limited resolution has prevented study of variability at wavelengths shorter than 100 km, where important eddy processes take place, ranging from energy dissipation to mixing and transport of water properties that are critical to understanding the ocean's roles in Earth's climate. The technology of radar interferometry promises to allow wide-swath measurement of sea surface height at a resolution that will resolve eddy structures down to 10 km. This approach holds the potential to meet the challenge of extending the observations to submesoscales and to set a standard for future altimetric measurement of the ocean.