This paper reviews the recent progress in our estimation of ocean dynamic topography and the derived surface geostrophic currents, mainly based on multiple nadir radar altimeter missions. These altimetric observations provide the cornerstone of our ocean circulation observing system from space. The largest signal in sea surface topography is from the mean surface dominated by the marine geoid, and we will discuss recent progress in observing the mean ocean circulation from altimetry, once the geoid and other corrections have been estimated and removed. We then address the recent advances in our observations of the large-scale and mesoscale ocean circulation from space, and the particular challenges and opportunities for new observations in the polar regions. The active research in the ocean barotropic tides and internal tidal circulation is also presented. The paper also addresses how our networks of global multi-satellite and in situ observations are being combined and assimilated to characterize the four-dimensional ocean circulation, for climate research and ocean forecasting systems. For the future of ocean circulation from space, the need for continuity of our current observing system is crucial, and we discuss the exciting enhancement to come with global wide-swath altimetry, the extension into the coastal and high-latitude regions, and proposals for direct total surface current satellites in the 2030 period.