The goal of cognitive neuroscience is to understand how mental operations are performed by the brain. Given the complexity of the brain, this is a challenging endeavor that requires the development of formal models. Here, we provide a perspective on models of neural information processing in cognitive neuroscience. We define what these models are, explain why they are useful, and specify criteria for evaluating models. We also highlight the difference between functional and mechanistic models, and call attention to the value that neuroanatomy has for understanding brain function. Based on the principles we propose, we proceed to evaluate the merit of recently touted deep neural network models. We contend that these models are promising, but substantial work is necessary to (i) clarify what type of explanation these models provide, (ii) determine what specific effects they accurately explain, and (iii) improve our understanding of how they work.