Our knowledge of the distribution and amount of terrestrial biomass is based almost entirely on ground measurements over an extremely small, and possibly biased sample, with many regions still unmeasured. Our understanding of changes in terrestrial biomass is even more rudimentary, although changes in land use, largely tropical deforestation, are estimated to have reduced biomass, globally. At the same time, however, the global carbon balance requires that terrestrial carbon storage has increased, albeit the exact magnitude, location, and causes of this residual terrestrial sink are still not well quantified. A satellite mission capable of measuring aboveground woody biomass could help reduce these uncertainties by delivering three products. First, a global map of aboveground woody biomass density would halve the uncertainty of estimated carbon emissions from land use change. Second, an annual, global map of natural disturbances could define the unknown but potentially large proportion of the residual terrestrial sink attributable to biomass recovery from such disturbances. Third, direct measurement of changes in aboveground biomass density (without classification of land cover or carbon modeling) would indicate the magnitude and distribution of at least the largest carbon sources (from deforestation and degradation) and sinks (from woody growth). The information would increase our understanding of the carbon cycle, including better information on the magnitude, location, and mechanisms responsible for terrestrial sources and sinks of carbon. This paper lays out the accuracy, spatial resolution, and coverage required for a satellite mission that would generate these products.