Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants) using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories--fear, anger, disgust, sadness, or happiness--is engaged by a study with 66% accuracy (43-86% across categories). Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a) differential patterns of involvement in neocortical systems that differ between humans and other species, and (b) distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches.