Since the 1980 eruption of Mount St. Helens, volcanologists have made considerable progress toward predicting eruptions on the basis of precursors that typically start a few days to several months in advance. Although accurate eruption prediction is by no means routine, it may now be possible in some cases to extend the effective warning period by anticipating the onset of short-term precursors. Three promising indicators of deep magmatic processes are (1) deep, long-period earthquakes and tremor that indicate the ascent of magma through the crust, (2) magmatic CO2 emission rate as a proxy for magma supply rate, and (3) relatively broad, generally aseismic surface uplift caused by magmatic intrusions. In the latter case it is essential to sample the deformation field thoroughly in both time and space to adequately constrain source models. Until recently, this has been nearly impossible because high-precision sensors could not be deployed in sufficient numbers, nor could extensive geodetic surveys be conducted often enough. Advances in instrumentation, interferometric synthetic aperture radar (InSAR), and telecommunications are helping to overcome these limitations. As a result, comprehensive geodetic monitoring of selected volcanoes is now feasible. A combination of InSAR, large-aperture GPS surveys, microgravity surveys, and dense arrays of continuous GPS stations, strain meters, and tiltmeters can reveal both spatial and temporal patterns of ground deformation throughout the eruption cycle. Improved geodetic monitoring of many of the world's volcanoes would be a major stride toward better understanding of magmatic processes and longer-term eruption forecasts.