The East Antarctic Ice Sheet (EAIS) is the largest continental ice mass on Earth, and documenting its evolution since the Last Glacial Maximum (LGM) is important for understanding its present-day and future behaviour. As part of a community effort, we review geological evidence from East Antarctica that constrains the ice sheet history throughout this period (similar to 30,000 years ago to present). This includes terrestrial cosmogenic nuclide dates from previously glaciated regions, C-14 chronologies from glacial and post-glacial deposits onshore and on the continental shelf, and ice sheet thickness changes inferred from ice cores and continental-scale ice sheet models. We also include new C-14 dates from the George V Land Terre Adelie Coast shelf. We show that the EAIS advanced to the continental shelf margin in some parts of East Antarctica, and that the ice sheet characteristically thickened by 300-400 m near the present-day coastline at these sites. This advance was associated with the formation of low-gradient ice streams that grounded at depths of >1 km below sea level on the inner continental shelf. The Lambert/Amery system thickened by a greater amount (800 m) near its present-day grounding zone, but did not advance beyond the inner continental shelf. At other sites in coastal East Antarctica (e.g. Bunger Hills, Larsemann Hills), very little change in the ice sheet margin occurred at the LGM, perhaps because ice streams accommodated any excess ice build up, leaving adjacent, ice-free areas relatively unaffected. Evidence from nunataks indicates that the amount of ice sheet thickening diminished inland at the LGM, an observation supported by ice cores, which suggest that interior ice sheet domes were similar to 100 m lower than present at this time. Ice sheet recession may have started similar to 18,000 years ago in the Lambert/Amery glacial system, and by similar to 14,000 years ago in Mac.Robertson Land. These early pulses of deglaciation may have been responses to abrupt sea-level rise events such as Meltwater Pulse la, destabilising the margins of the ice sheet. It is unlikely, however, that East Antarctica contributed more than similar to 1 m of eustatic sea-level equivalent to post-glacial meltwater pulses. The majority of ice sheet recession occurred after Meltwater Pulse la, between similar to 12,000 and similar to 6000 years ago, during a period when the adjacent ocean warmed significantly. Large tracts of East Antarctica remain poorly studied, and further work is required to develop a robust understanding of the LGM ice sheet expansion, and its subsequent contraction. Further work will also allow the contribution of the EAIS to post-glacial sea-level rise, and present-day estimates of glacio-isostatic adjustment to be refined.