Calving, or the release of icebergs from glaciers and floating ice shelves, is an important process transferring mass into the world's oceans. Calving glaciers and ice sheets make a large contribution to sea-level rise, but large uncertainty remains about future ice sheet response to alternative carbon scenarios. In this review, we summarize recent progress in understanding calving processes and representing them in the models needed to predict future ice sheet evolution and sea-level rise. We focus on two main types of calving models: (1) discrete element models that represent ice as assemblages of particles linked by breakable bonds, which can explicitly simulate fracture and calving processes; and (2) continuum models, in which calving processes are parameterized using simple calving laws. With a series of examples using both synthetic and real-world ice geometries, we show how explicit models are yielding a detailed, process-based understanding of system physics that can be translated into predictive capability via improved calving laws.