Artificial intelligence research on natural language understanding is discussed in this report using the notions that (1) natural language understanding systems must "see" sentences as elements whose significance resides in the contribution they make to the larger whole, and (2) a natural language understanding computer system must interpret each sentence with respect to both the linguistic context established by preceding sentences and the real-world setting. The first section provides an introduction to the term "discourse understanding" and to research on natural language understanding systems. The second section discusses modeling discourse structure, recent directions in this area (including discourse coherence, discourse structure and pronoun resolution, and context space theory), and the discourse structures theory, particularly the dynamic discourse model. Focusing on the meanings of the text, the third section considers truth conditions for sentence and text, consequences for logical formalisms, discourse anaphora, background knowledge and plausible inference, and summarizing stories. The fourth section addresses plan recognition, including speech acts, speech events, dialogue systems, and pragmatic perspective on discourse. The final section discusses modes of natural language. (Eight pages of references are included.) (JD)