The radiation stress concept is basic to the description of currents induced by waves. Gradients of the excess momentum flux due to the presence of waves (or radiation stress) appear as volume forces in the time- and depth-integrated horizontal momentum balance equations. Combined with the continuity equation these three equations yield the mean water surface elevation and both depth-averaged, horizontal velocity components. Since the introduction in 1969/1970 considerable progress has been made with the modelling of depthaveraged currents in the nearshore zone. In recent years, the modelling of wave-induced currents in the vertical crossshore plane has also made substantial progress. Here, the local time-averaged horizontal momentum equation describes the imbalance between the vertically nonuniform radiation stress and the vertically uniform pressure gradient. This imbalance induces a seaward directed undertow in the cross-shore direction, compensating for a shoreward mass flux above wave trough level. Latest developments are to combine the latter cross-shore flow field with the aforementioned horizontally two-dimensional flow field to a three-dimensional flow formulation.