Water waves in the ocean melt ice shelves and ice cliffs near the water line, which can destabilize the ice leading to calving events. Therefore, understanding and being able to predict how fast waves melt vertical ice cliffs is important for climate modelling. In this presentation, we report on new laboratory experiments and mathematical theory of these processes. We uncover a novel mechanism for how waves melt ice cliffs, develop a quantitative mathematical model for this mechanism, and conduct laboratory experiments and show that the data support the new model.