Intrusions of magma beneath volcanoes deform the surrounding rock and, if the intrusion is large enough, the overlying ground surface. Numerical models generally agree that, for most eruptions, subsurface volume changes are sufficient to produce measurable deformation at the surface. Studying this deformation can help to determine the location, volume, and shape of a subsurface magma body and thus to anticipate the onset and course of an eruption. This approach has been successfully applied at many restless volcanoes, especially basaltic shields and silicic calderas, using various geodetic techniques and sensors. However, its success at many intermediate-composition strato-volcanoes has been limited by generally long repose intervals, steep terrain, and structural influences that complicate the history and shape of surface deformation. These factors have made it difficult to adequately characterize deformation in space and time at many of the world's dangerous volcanoes. Recent technological advances promise to make this task easier by enabling the acquisition of geodetic data of high spatial and temporal resolution from Earth-orbiting satellites. Synthetic aperture radar interferometry (InSAR) can image ground deformation over large areas at metre-scale resolution over time-scales of a month to a few years. Global Positioning System (GPS) stations can provide continuous information on three-dimensional ground displacements at a network of key sites -information that is especially important during volcanic crises. By using InSAR to determine the shape of the displacement field and GPS to monitor temporal changes at key sites, scientists have a much better chance to capture geodetic signals that have so far been elusive at many volcanoes. This approach has the potential to provide longer-term warnings of impending volcanic activity than is possible with other monitoring techniques.