This paper reviews physical mechanisms, observation techniques and modelling approaches dealing with surface currents on short time scales (hours to days) relevant for operational oceanography. Key motivations for this article include fundamental difficulties in reliable measurements and the persistent lack of a widely held consensus on the definition of surface currents. These problems are augmented by the fact that various methods to observe and model ocean currents yield very different representations of a surface current. We distinguish between four applicable definitions for surface currents; (i) the interfacial surface current, (ii) the direct wind-driven surface current, (iii) the surface boundary layer current, and (iv) an effective drift current. Finally, we discuss challenges in synthesising various data sources of surface currents - i.e. observational and modelling – and take a view on the predictability of surface currents concluding with arguments that parts of the surface circulation exhibit predictability useful in an operational context.