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Both Martian polar regions are covered by prominent ice caps. Similar to snow on Earth, the seasonal caps are extended layers of CO2 frost which grow and shrink over the seasons. In the respective summer season, much smaller permanent caps remain, which are underlain by 3km high topographic domes termed as polar layered deposits. The polar layered deposits consist mainly of H2O ice and have formed by exchange of water with the atmosphere over at least millions of years. Alternating layers of clear and dusty ice, which are exposed in surface troughs and close to the margin, indicate a complex climatic history of Mars driven by quasiperiodic changes of orbital elements, similar to the Milankovitch cycles on Earth. Likely present-day glacial flow velocities are of the order of 0.1-1mma-1, the north polar deposits being more dynamic than the southern ones due to higher surface temperatures. Basal temperatures are far below the pressure melting point, with the possible exception of geothermally active areas under the ice.