This article discusses models of discourse processing, primarily from a psycholinguistic perspective, though considerations from the other cognitive sciences are mentioned where appropriate. It also touches on issues of discourse representation, because questions about representation and questions about process are closely intertwined. The origins of an interest in questions about discourse are identified in Bransford's ideas from the early 1970s. Their development into more detailed models of discourse processing is discussed, and detailed descriptions are given of, in particular, anaphor processing and, to a lesser extent the establishment of coherence. Some issues that arise in connection with the production of discourse are briefly discussed, as are their relation to dialog rather than to monolog.