Geological records from Tertiary and Quaternary terrestrial and oceanic sections have documented the presence of ice caps and sea ice covers both in the Southern and the Northern hemispheres since Eocene times, approximately since 45 Ma. In this paper focussing on Greenland we mainly use the occurrences of coarse ice-rafted debris (IRD) in Quaternary and Tertiary ocean sediment cores to conclude on age and origin of the glaciers/ice sheets, which once produced the icebergs transporting this material into the adjacent ocean. Deep-sea sediment cores with their records of ice-rafting from off NE Greenland, Fram Strait and to the south of Greenland suggest the more or less continuous existence of the Greenland ice sheet since 18 Ma, maybe much longer, and hence far beyond the stratigraphic extent of the Greenland ice cores. The timing of onset of glaciation on Greenland and whether it has been glaciated continuously since, are wide open questions of its long-term history. We also urgently need new scientific drilling programs in the waters around Greenland, in particular in the segment of the Arctic Ocean to the north of Greenland.