Language neuroscience has historically relied on highly controlled experimental paradigms that differ markedly from the conditions of real-world communication. Although such approaches have yielded important insights, they often fail to capture the integrative processes required for discourse and connected language. Here, we treat discourse as language extending beyond a single simple clause and used for a specific purpose. Recent advances in computational modeling, natural language processing, and neurophysiological measurement now make it possible to study language in more naturalistic, temporally extended, and ecologically valid contexts. In this closing editorial for a special issue of Cortex, we synthesize contributions that collectively argue for a discourse-centered neuroscience: the view that the neural basis of language becomes most fully visible when language is studied in its connected, purposeful form. We organize the issue around four broad themes—cortical topography and continuous integration, structural connectivity, large-scale network dynamics, and clinical mapping of language, thought, and interaction—and show how each reveals aspects of language organization that remain difficult to detect in isolated word- and sentence-level paradigms. We conclude by considering the implications of this work for basic and clinical science and by outlining future directions for the neurocognitive study of discourse.