The structure of forests, the three‐dimensional arrangement of individual trees, has a profound effect on how ecosystems function and cycle carbon, water, and nutrients. The increased need to understand local to global dynamics of ecosystems, a prerequisite to understand the coupling of the biosphere to other components of Earth systems, has created a demand for extensive ecosystem structure data. Repeated satellite observations of vegetation patterns in two dimensions have made significant contributions to our understanding of the state and dynamics of the global biosphere. Recent advances in remote sensing technology allow us to view the biosphere in three dimensions and provide us with refined measurements of horizontal, as well as vertical, structure of forests. This paper provides an introductory review of the importance of the three‐dimensional characterization of terrestrial ecosystem structure of forests and woodlands and its potential measurement from space. We discuss the relevance of these measurements for reducing the uncertainties of terrestrial carbon cycle and the response of ecosystems to future climate. By relating the 3‐D structure to forest biomass, carbon content, disturbance characteristics, and habitat diversity, we examine the requirements for future satellite sensors in terms of precision and spatial and temporal resolutions. In particular, we focus this review on measurements from lidar and radar sensors that provide vertical and horizontal characterization of vegetation and are currently recommended for next generation of NASA's Earth observing and European Earth Explorer systems.