During the last decade, significant progress has been made regarding the study of polar ice sheets and their interaction with the global climate system. This must to a large extent be due to the increased quantity of high-quality geophysical and glacial-geological observations. Equally important, however, is the crucial role being played by numerical ice-sheet models to interprete and link all these various pieces of information. The present-day generation of large-scale three-dimensional ice sheet models typically operate on horizontal grids of 20 to 40 km, have between 10 and 30 layers in the vertical and solve the fully coupled thermomechanic ice-flow equations.The most performant of these models are applied to the Greenland and Antarctic ice sheets, and are being employed to both examine the present state of these ice sheets and their response to changes in environmental conditions on time scales ranging from their inception during the Tertiary, their behaviour during the Quaternary ice ages and their response to future climatic warming.Current developments concentrate on a better description of boundary conditions and the interaction with the atmosphere, lithosphere, and ocean. In terms of ice-sheet variations, the surface mass-balance is often the most critical boundary condition, and here a lot is expected from combining ice-sheet models with General Circulation Models and more sophisticated mass-balance models in one or other way.During the talk, an overview will be given of the structure and physical basis of these ice-sheet models and of the type of problems which are addressed by them. Examples will be discussed of simulations of the Greenland and Antarctic ice sheets during the glacial cycles and of predictions of their future behaviour due to anthropogenic climatic change. This will be done within the context of the cryospheric contribution to global sea level changes.