Glaciers distinct from the Greenland and Antarctic ice sheets are currently losing mass rapidly with direct and severe impacts on the habitability of some regions on Earth as glacier meltwater contributes to sea-level rise and alters regional water resources in arid regions. In this review, we present the different techniques developed during the last two decades to measure glacier mass change from space: digital elevation model (DEM) differencing from stereo-imagery and synthetic aperture radar interferometry, laser and radar altimetry and space gravimetry. We illustrate their respective strengths and weaknesses to survey the mass change of a large Arctic ice body, the Vatnajökull Ice Cap (Iceland) and for the steep glaciers of the Everest area (Himalaya). For entire regions, mass change estimates sometimes disagree when a similar technique is applied by different research groups. At global scale, these discrepancies result in mass change estimates varying by 20%-30%. Our review confirms the need for more thorough inter-comparison studies to understand the origin of these differences and to better constrain regional to global glacier mass changes and, ultimately, past and future glacier contribution to sea-level rise.