Permafrost a common formation in the Arctic and Sub-arctic region: As a result of the strong negative temperature balance in the Polar region, almost 25 % of the land areas of the earth are underlain by permafrost. Permafrost dominates the landscape and ecosystems of the large tundra and boreal forest areas of Northern Eurasia and North America, where it can reach thicknesses of more than 1000 m. Formed in Siberia since the Late Pliocene, permafrost has the largest extension in lowland regions non-glaciated during the Pleistocene, where permafrost never disappeared completely during last warm phases. Due to the low global sea level in glacial periods, terrestrial permafrost has been formed on the large Arctic shelf, where now submerged subsea permafrost still exists as relict of up to 400 m depth below the sea bottom. The glacial-interglacial climate dynamics during the Quaternary are mirrored in permafrost and landscape dynamics in the Arctic and Subarctic. The relief of these regions is mainly controlled by periglacial and nival processes, where periglacial landforms are strongly connected to the formation or degradation of permafrost. Especially ice-rich permafrost is very sensitive to climate warming, which results in degradation processes, such as thermokarst, thermoerosion and coastal retreat. The observed warming of the Arctic results in an increasing of the active layer thickness, a rise in permafrost temperature, and in the disappearance of discontinuous permafrost at the southern boundary. The concurrent increase in the amounts of precipitation and melt water will further intensify thermokarst processes and thaw consolidation and will result in the formation of bogs and swamps. Permafrost degradation will result in complex changes of the geoecosystems, an increase of greenhouse gas emission due to enhanced organic matter decomposition, and a destabilization of permafrost regions, which are used by men for living and for economic use. Furthermore, anthropogenic activities lead to an additional destabilization of the thermal equilibrium of frozen ground affecting the stability of constructions and buildings.