Although aerial imagery has been used to support forestry for nearly a century, forest inventory is almost always conducted on the ground using conventional methods. Despite massive amounts of free remotely sensed imagery and the remarkable success of deep learning on related tasks, an automated, aerial inventory method has remained elusive. In this chapter we review the state of the art in forest inventory from remotely sensed imagery, promising approaches from the computer science literature, and potential future directions. We observe that the primary obstacle to accurate aerial forest inventory is the difficulty of manually delineating large numbers of tree crowns at a global scale, and discuss techniques from weakly supervised learning and natural language processing that can reduce human annotation and perhaps make a deep learning approach practical.