The last quarter century has provided extensive evidence that some regions of the human cortex are selectively engaged in processing a single specific domain of information, from faces, places, and bodies to language, music, and other people’s thoughts. This work dovetails with earlier theories in cognitive science highlighting domain specificity in human cognition, development, and evolution. But many questions remain unanswered about even the clearest cases of domain specificity in the brain, the selective engagement of the FFA, PPA, and EBA in the perception of faces, places, and bodies, respectively. First, these claims lack precision, saying little about what is computed and how, and relying on human judgements to decide what counts as a face, place, or body. Second, they provide no account of the reliably varying responses of these regions across different “preferred” images, or across different “nonpreferred” images for each category. Third, the category selectivity of each region is vulnerable to refutation if any of the vast set of as-yet-untested nonpreferred images turns out to produce a stronger response than preferred images for that region. Fourth, and most fundamentally, they provide no account of why, from a computational point of view, brains should exhibit this striking degree of functional specificity in the first place, and why we should have the particular visual specializations we do, for faces, places, and bodies, but not (apparently) for food or snakes. The advent of convolutional neural networks (CNNs) to model visual processing in the ventral pathway has opened up many opportunities to address these long-standing questions in new ways. I will describe ongoing efforts in our lab to harness CNNs to do just that.