This report develops a representation of focus of attention that circumscribes discourse contexts within a general representation of knowledge. Focus of attention is essential to any comprehension process because what and how a person understands is strongly influenced by where his attention is directed at a given moment. To formalize the notion of focus, the need for and the use of focus mechanisms are considered from the standpoint of building a computer system that can participate in a natural language dialogue with a user. Two ranges of focus, global and immediate, are investigated, and representations for incorporating them in a computer system are developed. The global focus in which an utterance is interpreted is determined by the total discourse and situational setting of the utterance. It influences what is talked about, how different concepts are introduced, and how concepts are referenced. To encode global focus computationally, a representation is developed that highlights those items that are relevant at a given place in a dialogue. The underlying knowledge representation is segmented into subunits, called focus spaces, that contain those items that are in the focus of attention of a dialogue participant during a particular part of the dialogue. Mechanisms are required for updating the focus representation, because, as a dialogue progresses, the objects and actions that are relevant to the conversation, and therefore in the participants' focus of attention, change. Procedures are described for deciding when and how to shift focus in task-oriented dialogues, i.e., in dialogues in which the participants are cooperating in a shared task. These procedures are guided by a representation of the task being performed. The ability to represent focus of attention in a language understanding system results in a new approach to an important problem in discourse comprehension -- the identification of the referents of definite noun phrases.