Currently, production and comprehension are regarded as quite distinct in accounts of language processing. In rejecting this dichotomy, we instead assert that producing and understanding are interwoven, and that this interweaving is what enables people to predict themselves and each other. We start by noting that production and comprehension are forms of action and action perception. We then consider the evidence for interweaving in action, action perception, and joint action, and explain such evidence in terms of prediction. Specifically, we assume that actors construct forward models of their actions before they execute those actions, and that perceivers of others' actions covertly imitate those actions, then construct forward models of those actions. We use these accounts of action, action perception, and joint action to develop accounts of production, comprehension, and interactive language. Importantly, they incorporate well-defined levels of linguistic representation. We show how speakers and comprehenders use covert imitation and forward modeling to make predictions at these levels of representation, how they interweave production and comprehension processes, and how they use these predictions to monitor the upcoming utterances. We show how these accounts explain a range of behavioral and neuroscientific data on language processing and discuss some of the implications of our proposal.