The article examines the problem of the relationship between ice caps and permafrost on the basis of the Pleistocene history of Asia. It is demonstrated that during the cryogenic epochs, and specifically during the period 30,000–16,000 years, B.P., permafrost covered a greater areal extent than ice sheets. The questions of the origin of major bodies of ground ice in the plains of Northern Eurasia, and of the cryogenic conditions during early stages of the geological history of the Earth are discussed. Cryological conditions prevailing on other planets in the solar system are also briefly discussed.