Tropical forests vary in composition, structure and function such that not all forests have similar ecological value. This variability is caused by natural and anthropogenic disturbance regimes, which influence the ability of forests to support biodiversity, store carbon, mediate water yield and facilitate human well-being. While international environmental agreements mandate protecting and restoring forests, only forest extent is typically considered, while forest quality is ignored. Consequently, the locations and loss rates of forests of high ecological value are unknown and coordinated strategies for conserving these forests remain undeveloped. Here, we map locations high in forest structural integrity as a measure of ecological quality on the basis of recently developed fine-resolution maps of three-dimensional forest structure, integrated with human pressure across the global moist tropics. Our analyses reveal that tall forests with closed canopies and low human pressure typical of natural conditions comprise half of the global humid or moist tropical forest estate, largely limited to the Amazon and Congo basins. Most of these forests have no formal protection and, given recent rates of loss, are at substantial risk. With the rapid disappearance of these 'best of the last' forests at stake, we provide a policy-driven framework for their conservation and restoration, and recommend locations to maintain protections, add new protections, mitigate deleterious human impacts and restore forest structure.