A review of wetting and drying (WD) algorithms used by contemporary numerical models based on the shallow water equations is presented. The numerical models reviewed employ WD algorithms that fall into four general frameworks: (1) Specifying a thin film of fluid over the entire domain; (2) checking if an element or node is wet, dry or potentially one of the two, and subsequently adding or removing elements from the computational domain; (3) linearly extrapolating the fluid depth onto a dry element and its nodes from nearby wet elements and computing the velocities; and (4) allowing the water surface to extend below the topographic ground surface. This review presents the benefits and drawbacks in terms of accuracy, robustness, computational efficiency, and conservation properties. The WD algorithms also tend to be highly tailored to the numerical model they serve and therefore difficult to generalize. Furthermore, the lack of temporally and spatially defined validation data has hampered comparisons of the models in terms of their ability to simulate WD over real domains. A short discussion of this topic is included in the conclusion. Copyright © 2012 John Wiley & Sons, Ltd.