Mapping and monitoring carbon stocks in forested regions of the world, particularly the tropics, has attracted a great deal of attention in recent years as deforestation and forest degradation account for up to 30% of anthropogenic carbon emissions, and are now included in climate change negotiations. We review the potential for satellites to measure carbon stocks, specifically aboveground biomass (AGB), and provide an overview of a range of approaches that have been developed and used to map AGB across a diverse set of conditions and geographic areas. We provide a summary of types of remote sensing measurements relevant to mapping AGB, and assess the relative merits and limitations of each. We then provide an overview of traditional techniques of mapping AGB based on ascribing field measurements to vegetation or land cover type classes, and describe the merits and limitations of those relative to recent data mining algorithms used in the context of an approach based on direct utilization of remote sensing measurements, whether optical or lidar reflectance, or radar backscatter. We conclude that while satellite remote sensing has often been discounted as inadequate for the task, attempts to map AGB without satellite imagery are insufficient. Moreover, the direct remote sensing approach provided more coherent maps of AGB relative to traditional approaches. We demonstrate this with a case study focused on continental Africa and discuss the work in the context of reducing uncertainty for carbon monitoring and markets.