Prediction is often regarded as an integral aspect of incremental language comprehension, but little is known about the cognitive architectures and mechanisms that support it. We review studies showing that listeners and readers use all manner of contextual information to generate multifaceted predictions about upcoming input. The nature of these predictions may vary between individuals owing to differences in language experience, among other factors. We then turn to unresolved questions which may guide the search for the underlying mechanisms. (i) Is prediction essential to language processing or an optional strategy? (ii) Are predictions generated from within the language system or by domain-general processes? (iii) What is the relationship between prediction and memory? (iv) Does prediction in comprehension require simulation via the production system? We discuss promising directions for making progress in answering these questions and for developing a mechanistic understanding of prediction in language.