Volume changes of the Greenland and Antarctic ice sheets constitute the largest source of uncertainty to explain the current rate of sea-level rise and have the potential to significantly increase this rate in future warmer climates. Crucial aspects are how climatic changes will affect the ice sheet's mass balance and how ice dynamics will react to the imposed environmental forcing. This is in addition to the longer-term background trend from adjustments as far back as the last glacial period and the possibility of unexpected ice-dynamic responses related to contemporary climate changes or not. In this review talk these questions are highlighted from a modeling point of view. Results will be discussed from 3-D thermomechanical ice sheet/ice shelf models coupled with climate models of varying complexity. It is found that the polar ice sheets may contribute more negatively to sea-level in the 21st century than previously thought, but would become dominant for sea-level rise after a few centuries, with the most important effect coming from the Greenland ice sheet. For the higher end of the range of currently available climate scenarios, the Greenland ice sheet is found to almost completely disappear within a period of about 1000 years, raising sea level by about 7 m. Furthermore, with the Greenland ice sheet removed, it would not regrow to its present state for present climate conditions, indicating hysteresis. There exists a point-of-no-return once Greenland ice sheet disintegration has set in beyond which complete removal of the ice sheet becomes irreversible, even if climatic conditions were to revert to present-day conditions. This point may already be reached after 250 years of ice-sheet melting under a medium greenhouse warming scenario. Model sumulations on the Antarctic ice sheet exhibit a more stable behaviour. A collapse of the marine West Antarctic Ice Sheet is considered unlikely during the coming centuries, not even for large warming and melting rates below the ice shelves of 10 m/year. For moderate warmings below some 5°C, the Antarctic ice sheet is found to grow as increases in snow accumulation outweigh the effects of increased runoff.