Glacier change is ubiquitous, but the fastest and largest magnitude changes occur in glaciers that terminate in water. This includes the most rapidly retreating glaciers, and also several advancing ones, often in similar regional climate settings. Furthermore, water-terminating glaciers show a large range in morphology, particularly when ice flow into ocean water is compared to that into freshwater lakes. All water-terminating glaciers share the ability to lose significant volume of ice at the front, either through mechanical calving or direct melt from the water in contact. Here we present a review of the subaqueous melt process. We discuss the relevant physics and show how different physical settings can lead to different glacial responses. We find that subaqueous melt can be an important trigger for glacier change. It can explain many of the morphological differences, such as the existence or absence of floating tongues. Subaqueous melting is influenced by glacial runoff, which is largely a function of atmospheric conditions. This shows a tight connection between atmosphere, oceans and lakes, and glaciers. Subaqueous melt rates, even if shown to be large, should always be discussed in the context of ice supply to the glacier front to assess its overall relevance. We find that melt is often relevant to explain seasonal evolution, can be instrumental in shifting a glacier into a different dynamical regime, and often forms a large part of a glacier's mass loss. On the other hand, in some cases, melt is a small component of mass loss and does not significantly affect glacier response.