Abstract The NASA/CNES Surface Water and Ocean Topography (SWOT) swath‐mapping radar altimetry satellite mission, launched in December 2022, provides repeat‐track coverage to about ±78.2° latitude every 21 days, sampling many of Antarctica’s most dynamic ice shelves that play key roles in constraining mass loss from the grounded ice sheet. Understanding how ice‐shelf extent and thickness respond to forcings requires three‐dimensional mapping of ice structure at the short time and space scales of major mass change processes including basal and surface mass balances, and crevasse growth. We demonstrate that repeated SWOT high‐rate acquisitions can accurately monitor changes in ice‐shelf surface heights, revealing key processes including responses to ocean tides and atmospheric forcing, ice flexure along grounding zones, and crevasse deepening, that affect stresses impacting ice loss. Despite limitations in acquisition and processing, some of which are being addressed, the SWOT mission provides exciting new opportunities for studying ice‐shelf dynamics.