The largest environmental changes in the recent geological history of the Earth are undoubtedly the successions of glacial and interglacial times. It has been clearly demonstrated that changes in the orbital parameters of our planet have a crucial role in these cycles. Nevertheless, several problems in classical astronomical theory of paleoclimate have indeed been identified: (1) The main cyclicity in the paleoclimatic record is close to 100,000 years, but there is no significant orbitally induced changes in the radiative forcing of the Earth in this frequency range (the 100-kyr problem); (2) the most prominent glacial-interglacial transition occurs at a time of minimal orbital variations (the stage 11 problem); and (3) at ~0.8 Ma a change from a 41-kyr dominant periodicity to a 100-kyr periodicity occurred without major changes in orbital forcing or in the Earth's configuration (the late Pleistocene transition problem). Additionally, the traditional view states that the climate system changes slowly and continuously together with the slow evolution of the large continental ice sheets, whereas recent high-resolution data from ice and marine sediment cores do not support such a gradual scenario. Most of the temperature rise at the last termination occurred over a few decades in the Northern Hemisphere, indicating a major and abrupt reorganization of the ocean-atmosphere system. Similarly, huge iceberg discharges during glacial times, known as Heinrich events, clearly demonstrate that ice sheet changes may also be sometimes quite abrupt. In light of these recent paleoclimatic data the Earth climate system appears much more unstable and seems to jump abruptly between different quasi steady states. Using the concept of thresholds, this new paradigm can be easily integrated into classical astronomical theory and compared with recent observational evidence. If the ice sheet changes are, by definition, the central phenomenon of glacial-interglacial cycles, other components of the climate system (atmospheric CO2 concentration, Southern Ocean productivity, or global deep-ocean circulation) may play an even more fundamental role in these climatic cycles. ¿ 2001 American Geophysical Union