The climatic conditions in the Arctic, and observations of the wind-induced drift of ice made in connexion with Fridtjof Nansen's Fram expedition, led to the discovery 100 years ago by Vilhelm Bjerknes' pupil, V.W. Ekman, of the importance of the Earth's rotation in limiting the depth of the wind-induced shear current in the ocean. This essay commemorates the centenary of Ekman's seminal paper, which was published in 1905. The paper presents a concise summary of Ekman's contributions to physical oceanography and a brief review of their continuing impact. The two key concepts are the Ekman spiral (the helical rotation of the velocity vector, in atmospheric and oceanic boundary layers) and the resultant Ekman pumping (vertical motions in the water column associated with the divergence of the flow in the surface layer in the presence of a rotational wind-stress field). Later work has revealed how the magnitude and direction of the surface current relative to the wind vector is influenced by the presence of surface waves and the behaviour of the turbulent flow in the near-surface layer of the ocean. However, the structure of Ekman's original viscous coupling model remains a permanent legacy to physical oceanographers.