This chapter reviews the contribution of satellite altimetry to the observation and understanding of ocean currents and eddies. It focuses on mesoscale variability which is the dominant signal of the ocean circulation and is a crucial component of its dynamics. After a general introduction on mesoscale variability in section 1, section 2 discusses specific issues for altimeter data processing which are necessary for mesoscale studies including merging, sampling and velocity estimation. Section 3 deals with the description of ocean currents. We review first some of the main techniques used to estimate the absolute velocities and transports from altimeter data. We then look at each major current system separately, and review the considerable progress made by altimetric studies in each of the main western boundary currents, eastern boundary currents, open ocean currents, and in the semi-enclosed seas. Section 4 provides a global statistical description of mesoscale variability which is a unique contribution of satellite altimetry. Studies dealing with the geographical and seasonal to interannual variations in eddy intensity are analyzed. We also summarize the main findings on space and time scales of mesoscale variability and the relationship between spatial scales and the internal Rossby radius. We then proceed to the analysis of frequency and wavenumber spectra and the relationship with quasi-gesotrophic turbulence theories. Studies which compare these eddy statistics with eddy resolving model simulations are also summarized. Eddy dynamics (eddy/mean flow interaction, eddy transport and eddy diffusivity) are finally discussed.