The last few decades have witnessed several major programs aimed at investigating the Greenland Ice Sheet. These programs have greatly improved our knowledge of the ice sheet in terms of topography, ice thickness, ice temperature, flow, and mass balance. It is concluded that presently the Greenland Ice Sheet as a whole is close to a balanced state, the slight thinning of some marginal sectors likely being compensated for by a slight thickening in the central area. The information on the dynamic and climatic history of the ice sheet as retrieved from the deep ice cores drilled at Camp Century and Dye 3, is reviewed; the problems involved in interpreting ice core records and the main results of the studies — derived past temperatures, precipitation rates, records of past volcanism — are presented. Whereas major changes in global climate are unambiguously revealed by the ice core records, changes of smaller amplitude and shorter duration seem to be more difficult to extract, probably due to a rather high noise level combined with disturbances induced by the flow of the ice. To correct for the latter effect, modelling of the ice sheet flow is needed. New important information on the internal deformations of the ice sheet has been obtained from measurements in the deep drill holes and from deformation tests on core ice. This information has significantly improved dynamic models for the ice sheet and thus has helped to interpret the environmental records from the ice cores. Recent work aimed at collecting paleoenvironmental information from the marginal sectors of the ice sheet is also reviewed. Even though the records that can be retrieved from the ice margin are not as detailed as ice core records, studies on the ice margin seem to have a great potential for obtaining an overview on a regional basis of the dynamic and climatic history of the ice sheet.