The long duration and low noise level offered by the US Navy's Geosat altimeter opened up new scope for the quantitative use of satellite altimetry in observing oceanic mesoscale variability. This paper, centered on recent results from Geosat data, shows how satellite altimetry contributes to the description of oceanic mesoscale variability. The methods commonly used to extract the oceanic mesoscale signal are first recalled. We briefly discuss their impact on the signal, and measurement errors. We then look at the results of comparisons between altimeter data and in situ measurements, and demonstrate that Geosat data are suitable for observing mesoscale variability. The unique contribution which altimetry can make comes from its global space-time coverage, which provides a quasi-synoptic description of the ocean circulation and a statistical description to an unrivalled degree of detail. A few examples illustrate the innovative contribution which synoptic mapping can provide. But the greatest contribution is in the statistical description of ocean mesoscale variability. We review several papers dealing with the global statistical description of mesoscale variability and its seasonal variations, characterization of space and time scales and frequency-wave number spectral analysis, and statistical descriptions of western boundary currents. All confirm the unique contribution which satellite altimetry can make to the statistical description of mesoscale phenomena.