While a semantics without differing "points of view" of different agents is a good first hypothesis for the analysis of the content of monologue, dialogues typically involve differing points of view from different agents. In particular one agent may not agree with what another agent asserts, or may have a different interpretation of an utterance from that of its author. An adequate semantics for dialogue should proceed by attributing to different dialogue agents separate views of the contents of their conversation. We model this, following others, by assigning each agent her own commitment slate. In this paper we bring out a complication with this approach that has gone so far unnoticed in formal semantics and the prior work we just mentioned, albeit it is well-known from epistemic game theory: commitment slates interact; agents typically commit to the fact that other agents make certain commitments. We thus formulate the semantics of dialogue moves and conversational goals in terms of nested, public commitments. We develop two semantics for nested commitments, one for a simple propositional language, the other for a full description language for the discourse structure of dialogues; and we show how one is an approximation of the other. We apply this formal setting to provide a unified account of different linguistic problems: the problem of ambiguity and the problem of acknowledgments and grounding. We also briefly discuss the problem of corrections and how to integrate them in our framework.