Glaciological models have an important role to integrate the various pieces of palaeoclimatic information, to interpret the glacial-geological record in terms of climatic and ice-dynamic processes and to establish the ice thickness distribution over time, which can usually not be derived directly from observations. This talk will primarily review model simulations of the Antarctic and Greenland ice sheets during the last few glacial cycles obtained from three-dimensional thermomechanical models. These models freely generate ice-sheet volume and extent and are driven by changes of temperature, mass balance, and sea-level. The emphasis will be on reconstructions of the LGM and on a discussion of a series of sensitivity experiments dealing with (i) the temperature forcing as derived from ice cores, (ii) the treatment of accumulation changes, (iii) basal sliding, (iv) the speed of isostatic adjustment, (v) the role of thermomechanical coupling, and (vi) viscosity changes and the rate of basal melting below Antarctic ice shelves.For the Antarctic ice sheet, we generally find that changes in the ice shelf have an important control on the position of the grounding line at the LGM and that in most runs the deglaciation of the Ross and Weddell basins occurs after 10000 years BP to be nearly completed by the present time. The ice over central East Antarctica is generally thinner during glacial periods than today leading to an overall Antarctic contribution to sea-level lowering at the LGM of about 15-20 m, significantly less than the older CLIMAP reconstructions.Boundary conditions for modelling the Greenland ice sheet appear to be better constrained and the most sensitive period concerns the size of the ice sheet during the Eemian. For the LGM, almost all of the runs show a maximum extent close to the continental break together with a thinning of the central areas by up to several hunded meters. It is unlikely that the Greenland ice sheet has contributed more than 2-3 meters to the sea-level lowering at the LGM.Techniques similar to those used to model the Antarctic and Greenland ice sheets have on the other hand generally failed to model the large Quaternary ice sheets of the northern hemisphere continents in good agreement with the glacial-geological record. The main reason is the difficulty of prescribing the evolution of mass-balance conditions at the surface, but also basal conditions and marine interactions at their Arctic margins appear difficult to model. Nevertheless, simple experiments have provided useful insights in thresholds for growth and decay and general physical characteristics and some of these results will also be shown.