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 a crowdsourcing platform for collecting large amounts of drawing and recognition data, and applied a deep neural network model of visual cortex to explore the hypothesis that drawing recruits the same abstract object representations that subserve visual recognition. Consistent with this hypothesis, we discovered that drawings contain the features most important for recognizing objects in photographs, and that learning to make more recognizable drawings of objects generalizes to 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.