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Synthetic aperture radar interferometry (InSAR) from Earth-orbiting spacecraft provides a new tool to map global topography and deformation of the Earth’s surface. Radar images taken from slightly different viewing directions allow the construction of digital elevation models of meter-scale accuracy. These data sets aid in the analysis and interpretation of tectonic and volcanic landscapes. If the Earth’s surface deformed between two radar image acquisitions, a map of the surface displacement with tens-of-meters resolution and subcentimeter accuracy can be constructed. This review gives a basic overview of InSAR for Earth scientists and presents a selection of geologic applications that demonstrate the unique capabilities of InSAR for mapping the topography and deformation of the Earth.