The Earth’s climate is changing and during the last 30 years the extent of the sea-ice has been decreasing steadily. At the same time the major icecaps in Greenland and Antarctica have experienced an increased melt. The extent of the sea-ice can be determined quite accurately with current satellite observations, but the thickness and thereby the mass of the sea-ice is subject to large uncertainties. Satellite observations of the icecaps are also affected by errors in the margin zones, where the largest changes takes place. The development of a new type of radar altimeter, named the SAR altimeter, provides the possibility of observing the icecaps and the sea-ice with a much higher resolution than previously. In this thesis SAR altimetry data from CryoSat-2 and the airborne ASIRAS instrument have been used to demonstrate the possibilities in the new observations. Using a new method developed during the PhD it is possible to determine the depth of annual layers in the snow on the icecap of Greenland from ASIRAS data. From these annual layers it is possible to estimate the accumulation, which is an important parameter for the precise determination and modelling of changes in the mass of the icecap. Furthermore, a method has been developed to separate radar signals returned by ice floes from radar signals returned from the sea between the ice floes. When heights measured over ice floes and heights measured over ocean can be separated, the height by which the ice floe is above the sea surface can be determined and hereby the thickness of the entire ice floe. This allows the entire mass of the sea-ice to be determined much more accurately than previously.