Spaceborne altimetry with measurement acccuracies of a few centimeters has the potential for determining sea surface elevations necessary to compute three-dimensional geostrophic currents from traditional hydrographic observations. The existing limitation in this approach is the uncertainty in our knowledge of the global and ocean geopotentials that produce satellite and geoid height uncertainties about an order of magnitude larger than the goal of about 10 cm. This paper begins with a description of the quantitative effects of geopotential uncertainties on processing altimetry data. This is followed by a review of existing models, which are shown to be inadequate. Potential near-term improvements not requiring additional spacecraft are discussed. However, even though there would be substantial improvements at the longer wavelength, the oceanographic goal would not be achieved. The potential NASA Geopotential Research Mission (GRM) is described. This mission should produce geopotential models that are capable of defining the ocean geoid to 10 cm and near-earth satellite positions significantly better. For completeness the state of the art and the potential of spaceborne gravity gravimetry is described as an alternative approach to improve our knowledge of the geopotential.