This paper examines the task of understanding dialogues in terms of the mental states of the participating agents. It presents a motivating example that clarifies the challenges this problem involves and then outlines a theory of dialogue interpretation based on abductive inference of these unobserved beliefs and goals, incremental construction of explanations, and reliance on domain-independent knowledge. After this, it describes UMBRA, an implementation of the theory that embodies these assumptions. Experiments with the system are reported that demonstrate its ability to accurately infer the conversants’ mental states even when some speech acts are unavailable. The conclusion reviews related research on dialogue and discusses avenues for future study.