This chapter reviews progress made by brain-reading (neurosemantic) studies that use multivariate analytic methods to delineate the nature, content, and neuroanatomical distribution of the neural representation of concept knowledge in semantic memory. Concept knowledge underlies almost all human thought, communication, and daily activity. The chapter describes how neurosemantic research has provided initial answers to such prominent questions as: What types of information are encoded in a given neural concept representation? To what extent are neural concept representations common across different people? Do neural concept representations evoked by pictures differ from those evoked by language? How are abstract versus concrete concepts represented in the brain? How does the neural representation of a concept evolve while a new concept is being learned? What are the properties and implications of the data analytic techniques that are used in this research area? The initial answers to these questions illuminate how the properties of brain organization impose a structure on the neural representations of concepts.