Multichannel ice-penetrating radar systems can be used to generate radar volumes: three-dimensional data structures that capture variability in backscattering intensity as a function of along-track position, two-way travel time and elevation angle. By digitizing surfaces within these data volumes, the production of wide-area, fine-resolution digital elevation models (DEMs) of the ice-bottom interface (measured through kilometres of ice) is now possible. This paper reviews this technique ('radar swath imaging'), explores its methodological principles, describes its operational requirements and highlights recent scientific advances enabled by radar swath imaging. Observations of glacier and substrate morphology and physical properties inferred from swath data have already been used to improve our understanding of ice-shelf melt, basal sliding and subglacial sediment and water transport. Lessons learned from these initial surveys should inform future data collection strategies, so that radar swath imaging can be deployed in the most productive way possible during upcoming major field campaigns, including the Fifth International Polar Year and beyond. This article is part of the Theo Murphy meeting issue 'Next generation ice-sheet bed measurements'.