Recent technological advances in the study and dating of both land and marine glacial geologic features combined with improvements in both glaciological and post-glacial isostatic rebound modelling have led to significant improvements in our knowledge and understanding of the Antarctic Ice Sheets at the Last Glacial Maximum (LGM) and their subsequent changes throughout the Holocene. Here we review the geological evidence for the extent and timing of the maximum advance of the East and West Antarctic Ice Sheets and the ice cover of the Antarctic Peninsula during the most recent glacial cycle. We also discuss evidence for the rate and timing of Holocene Ice Sheet retreat. Geological data provide a very important 'first-hand' record of ice-sheet changes over a range of time periods. They are also useful for constraining and improving models which then have the potential to both fill in the gaps for which geological data are unavailable, and to make predictions of the future. Inspection of the geological record allows us to form qualitative scenarios concerning glacial history. Numerical modelling has been used on several occasions to test such hypotheses. We discuss such numerical studies, indicating both their importance and limitations in order to develop quantitative ideas about the late Quaternary history of the ice sheet. An important environmental aspect of Antarctica's glacial history is its contribution to global sea level rise since the LGM. The past decade has seen the range of estimates (from reconstructions based solely on geological evidence, on glaciological modelling constrained by geology and on modelling of the isostatic rebound) change from 0.5-38 m sea level equivalent to 5.9-19.2 m. Although the convergence of estimates is encouraging, there is a need for further glaciological modelling to take full account of the constraints placed on LGM ice expansion, particularly in East Antarctica, by new geological evidence.