Production and comprehension have long been viewed as inseparable components of language. The study of vision, by contrast, has centered almost exclusively on comprehension. Here we investigate drawing--the most basic form of visual production. How do we convey concepts in visual form, and how does refining this skill, in turn, affect recognition? We developed an online platform for collecting large amounts of drawing and recognition data, and applied a deep convolutional neural network model of visual cortex trained only on natural images to explore the hypothesis that drawing recruits the same abstract feature representations that support natural visual object recognition. Consistent with this hypothesis, higher layers of this model captured the abstract features of both drawings and natural images most important for recognition, and people learning to produce more recognizable drawings of objects exhibited enhanced recognition of those objects. These findings could explain why drawing is so effective for communicating visual concepts, they suggest novel approaches for evaluating and refining conceptual knowledge, and they highlight the potential of deep networks for understanding human learning.