Direct measurement of large-scale ocean currents with current meter arrays is difficult and costly on basin scales. Since large-scale currents are very nearly in geostrophic balance, their velocity can be calculated from the pressure gradient on an equigeopotential surface. The surface geostrophic current therefore can be calculated from the deviation of sea level from the equigeopotential at the ocean surface (the marine geoid). Measuring sea level from space by satellite altimetry thus offers a unique opportunity for determining the global surface geostrophic ocean circulation and its variability. Coupled with knowledge of the geoid and the ocean density field, satellite altimetry provides the only feasible approach for determining absolute geostrophic currents in the global ocean. Repeated altimetric observations of sea level at the same locations can resolve the variability of surface geostrophic currents, without the requirement for an accurate geoid model. In this paper, we briefly introduce the technique of satellite altimetry, highlight progress made in the past, assess the challenges that lie ahead, and discuss future plans.