The meaning of language is represented in regions of the cerebral cortex collectively known as the 'semantic system'. However, little of the semantic system has been mapped comprehensively, and the semantic selectivity of most regions is unknown. Here we systematically map semantic selectivity across the cortex using voxel-wise modelling of functional MRI (fMRI) data collected while subjects listened to hours of narrative stories. We show that the semantic system is organized into intricate patterns that seem to be consistent across individuals. We then use a novel generative model to create a detailed semantic atlas. Our results suggest that most areas within the semantic system represent information about specific semantic domains, or groups of related concepts, and our atlas shows which domains are represented in each area. This study demonstrates that data-driven methods--commonplace in studies of human neuroanatomy and functional connectivity--provide a powerful and efficient means for mapping functional representations in the brain.