Forests are the dominant terrestrial ecosystem on Earth. We review the environmental factors controlling their structure and global distribution and evaluate their current and future trajectory. Adaptations of trees to climate and resource gradients, coupled with disturbances and forest dynamics, create complex geographical patterns in forest assemblages and structures. These patterns are increasingly discernible through new satellite and airborne observation systems, improved forest inventories, and global ecosystem models. Forest biomass is a complex property affected by forest distribution, structure, and ecological processes. Since at least 1990, biomass density has consistently increased in global established forests, despite increasing mortality in some regions, suggesting that a global driver such as elevated CO2 may be enhancing biomass gains. Global forests have also apparently become more dynamic. Advanced information about the structure, distribution, and biomass of the world's forests provides critical ecological insights and opportunities for sustainable forest management and enhancing forest conservation and ecosystem services.