Theoretical advances in language research and the availability of increasingly high-resolution experimental techniques in the cognitive neurosciences are profoundly changing how we investigate and conceive of the neural basis of speech and language processing. Recent work closely aligns language research with issues at the core of systems neuroscience, ranging from neurophysiological and neuroanatomic characterizations to questions about neural coding. Here we highlight, across different aspects of language processing (perception, production, sign language, meaning construction), new insights and approaches to the neurobiology of language, aiming to describe promising new areas of investigation in which the neurosciences intersect with linguistic research more closely than before. This paper summarizes in brief some of the issues that constitute the background for talks presented in a symposium at the Annual Meeting of the Society for Neuroscience. It is not a comprehensive review of any of the issues that are discussed in the symposium.