Recent studies have integrated noninvasive brain-imaging methods and advanced analysis techniques to study associations between the location of brain damage and cognitive deficits. By applying data-driven analysis methods to large sets of data on language deficits after stroke (aphasia), these studies have identified the cognitive systems that support language processing—phonology, semantics, fluency, and executive functioning—and their neural basis. Phonological processing is supported by dual pathways around the Sylvian fissure, a ventral speech-recognition component and a dorsal speech-production component; fluent sentence-level speech production relies on a more anterior frontal component, and the semantic system relies on a hub in the anterior temporal lobe and frontotemporal white-matter tracts. The executive function system was less consistently localized, possibly because of the kinds of brain damage tested in these studies. This review synthesizes the results of these studies, showing how they converge with contemporary models of primary systems that support perception, action, and conceptual knowledge across domains, and highlights some divergent findings and directions for future research.