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GRACE time-variable gravity fields provide a means of measuring temporal and spatial variations of mass redistribution within the Earth system. The GRACE mission has launched a new era in studying a series of geophysical problems ranging from deep Earth structure to tracking mass redistribution on and near the surface of the Earth. GRACE has greatly improved understanding of mass redistribution in various compartments of the climate system (atmosphere, oceans, terrestrial water, and cryosphere). In this review, we use examples to show how GRACE has fundamentally enriched a number of fields, including (but not limited to) the global water cycle and land hydrology, mass balance of polar ice sheets and mountain glaciers, ocean mass and global sea level change, and solid Earth geophysics. (c) 2010 Elsevier B V. All rights reserved