The largest uncertainty in future sea-level rise is loss of ice from the Greenland and Antarctic Ice Sheets. Ice shelves, freely floating platforms of ice that fringe the ice sheets, play a crucial role in restraining discharge of grounded ice into the ocean through buttressing. However, since the 1990s, several ice shelves have thinned, retreated, and collapsed. If this pattern continues, it could expose thick cliffs that become structurally unstable and collapse in a process called marine ice cliff instability (MICI). However, the feedbacks between calving, retreat, and other forcings are not well understood. Here we review observed modes of calving from ice shelves and marine-terminating glaciers, and their relation to environmental forces. We show that the primary driver of calving is long-term internal glaciological stress, but as ice shelves thin they may become more vulnerable to environmental forcing. This vulnerability—and the potential for MICI—comes from a combination of the distribution of preexisting flaws within the ice and regions where the stress is large enough to initiate fracture. Although significant progress has been made modeling these processes, theories must now be tested against a wide range of environmental and glaciological conditions in both modern and paleo conditions. ▪Ice shelves, floating platforms of ice fed by ice sheets, shed mass in a near-instantaneous fashion through iceberg calving.▪Most ice shelves exhibit a stable cycle of calving front advance and retreat that is insensitive to small changes in environmental conditions.▪Some ice shelves have retreated or collapsed completely, and in the future this could expose thick cliffs that could become structurally unstable called ice cliff instability.▪The potential for ice shelf and ice cliff instability is controlled by the presence and evolution of flaws or fractures within the ice.