This thesis investigates the use of satellite altimetry techniques for measuring surface elevation changes of ice caps. Two satellite altimeters, Radar Altimeter 2 (RA-2) and Geoscience Laser Altimeter System (GLAS) are used to assess the surface elevation changes of three Arctic ice caps. This is the first time the RA-2 has been used to assess the elevation changes of ice caps - targets much smaller than the ice sheets which are the instrument’s primary land ice targets. Algorithms for the retrieval of elevation change rates over ice caps using data acquired by RA-2 and GLAS are presented. These algorithms form a part of a European Space Agency (ESA) glacier monitoring system GlobGlacier. A comparison of GLAS elevation data to those acquired by the RA-2 shows agreement between the two instruments. Surface elevation change rate estimates based on RA-2 are given for three ice caps: Devon Ice Cap in Arctic Canada (−0.09 ± 0.29 m/a), Flade Isblink in Greenland (0.03 ± 0.03 m/a) and Austfonna on Svalbard (0.33 ± 0.08 m/a). Based on RA-2 and GLAS measurements it is shown that the areas of Flade Isblink below the late summer snow line have been thinning whereas the areas above the late summer snow line have been thickening. Also GLAS observed dynamic thickening rates of more than 3 m/a are presented. On Flade Isblink and Austfonna RA-2 measurements are compared to surface mass balance (SMB) estimates from a regional atmospheric climate model RACMO2. The comparison shows that SMB is the driver of interannual surface elevation changes at Austfonna. In contrast the comparison reveals areas on Flade Isblink where ice dynamics have an important effect on the surface elevation. Furthermore, RACMO2 estimates of surface mass budget at Austfonna before the satellite altimeter era are presented. This thesis shows that both traditional radar and laser satellite altimetry can be used to quantify the response of ice caps to the changing climate. Direct altimeter measurements of surface elevation and, in consequence volume change of ice caps, can be used to improve their mass budget estimates.