Attenuation of surface waves due to viscous dissipation is accompanied by the excitation of slow vortex currents due to the conservation of total momentum. We present a theoretical model for small-amplitude waves that explains experiments on vortex flow generation by crossing waves. Special attention is paid to the effect of surface contaminants, which is accounted for within the framework of a model of a thin elastic liquid film, leading to enhanced wave dissipation and intensified vortex currents. As the amplitude of the currents increases, their interaction with the waves must be considered. A theoretical framework is proposed to describe this interaction, demonstrating its applicability to classical problems: Guyon waves, the propagation of short waves against a current, and Langmuir circulation. Finally, experimental data on the turbulent regime of flow generation, which occurs at sufficiently large wave amplitudes, are described, and open questions in this field are outlined.