We use a concept of framing to explain 3 cases in which participants initially lacked mutual understanding but then achieved significant mutual understanding. The cases were all consistent with a pattern of "positional framing" that includes a human participant who is inquiring, which we call a "listener", and a "source", which may be another human participant or a non-human system. Participants with these different positionings have different perspectives that shape the interpretations and functions of their contributions. We hypothesize that achievement of mutual understanding also depends on participants having "epistemological" and "conceptual framings" that are sufficiently aligned. We distinguish between cases in which the participants achieved alignment of conceptual framing by adopting a schema that was in their common ground, cases in which the participants co-constructed a coherent framing without the benefit of a prefabricated schema (by constraint satisfaction, we hypothesize), and cases in which mutual understanding involved a refinement that did not require reframing. We argue that our hypotheses qualify as explanatory mechanisms, and we explicate this in an appendix. Our general goal is to contribute to the growing body of scientific studies that include concepts and methods for understanding cognitive structures and processes integrated with concepts and methods for understanding interaction that people have with each other and with other material and informational systems. [Supplementary materials are available for this article. Go to the publisher's online edition of the "Journal of the Learning Sciences" for the following free supplemental resource: "A Mechanistic Analysis of Discourse," which presents an analysis of an episode from Case #1 of this article as a more detailed example of the kind of mechanism we have hypothesized in our more general accounts of interaction presented in the article.] (Contains 8 tables, 9 figures and 12 footnotes.)