Ocean currents play a key role in Earth’s climate, they are of major importance for navigation and human activities at sea, and impact almost all processes that take place in the ocean. Nevertheless, their observation and forecasting are still difficult. First, direct measurements of ocean currents are difficult to obtain synoptically at global scale. Consequently, it has been necessary to use Sea Surface Height and Sea Surface Temperature measurements and refer to dynamical frameworks to derive the velocity field. Second, the assimilation of the velocity field into numerical models of ocean circulation is difficult mainly due to lack of data. Recent experiments assimilating coastal-based radar data have shown that ocean currents will contribute to increase the forecast skill of surface currents, but require to be applied in multi-data assimilation approaches to allow better identification of the thermohaline structure of the ocean. In this paper we review the current knowledge on these fields and provide global and systematic view on the technologies to retrieve ocean velocities in the upper ocean and the available approaches to assimilate this information into ocean model.