The interactive-alignment account of dialogue proposes that interlocutors achieve conversational success by aligning their understanding of the situation under discussion. Such alignment occurs because they prime each other at different levels of representation (e.g., phonology, syntax, semantics), and this is possible because these representations are shared across production and comprehension. In this paper, we briefly review the behavioral evidence, and then consider how findings from cognitive neuroscience might lend support to this account, on the assumption that alignment of neural activity corresponds to alignment of mental states. We first review work supporting representational parity between production and comprehension, and suggest that neural activity associated with phonological, lexical, and syntactic aspects of production and comprehension are closely related. We next consider evidence for the neural bases of the activation and use of situation models during production and comprehension, and how these demonstrate the activation of non-linguistic conceptual representations associated with language use. We then review evidence for alignment of neural mechanisms that are specific to the act of communication. Finally, we suggest some avenues of further research that need to be explored to test crucial predictions of the interactive alignment account.