Our understanding of processes relating to the retreat of marine‐based ice sheets, such as the West Antarctic Ice Sheet and tidewater‐terminating glaciers in Greenland today, is still limited. In particular, the role of ice stream instabilities and oceanographic dynamics in driving their collapse are poorly constrained beyond observational timescales. Over numerous glaciations during the Quaternary, a marine‐based ice sheet has waxed and waned over the Barents Sea continental shelf, characterized by a number of ice streams that extended to the shelf edge and subsequently collapsed during periods of climate and ocean warming. Increasing availability of offshore and onshore geophysical data over the last decade has significantly enhanced our knowledge of the pattern and timing of retreat of this Barents Sea ice sheet (BSIS), particularly so from its Late Weichselian maximum extent. We present a review of existing geophysical constraints that detail the dynamic evolution of the BSIS through the last glacial cycle, providing numerical modelers and geophysical workers with a benchmark data set with which to tune ice sheet reconstructions and explore ice sheet sensitivities and drivers of dynamic behavior. Although constraining data are generally spatially sporadic across the Barents and Kara Seas, behaviors such as ice sheet thinning, major ice divide migration, asynchronous and rapid flow switching, and ice stream collapses are all evident. Further investigation into the drivers and mechanisms of such dynamics within this unique paleo‐analogue is seen as a key priority for advancing our understanding of marine‐based ice sheet deglaciations, both in the deep past and in the short‐term future.