The semantics of dialogue is a fundamental topic for a number of reasons. First, dialogue is the primary medium of language use, phylogenetically and ontogenetically. Second, studying dialogue forces one to a particularly careful study of the nature of context. The context has a role to play in determining what one can or should say at a given point and also how to say it. Conversely, it affords the interlocutors a very impressive economy of expression – there is much subtlety that can be achieved with relatively little effort drawing simply on material that is in the context. Consequently, two themes will drive this article, relating to two fundamental problems a semantic analysis in dialogue has to tackle: (1) Conversational relevance: given that a conversation is in a certain state, what utterances can be produced coherently by each conversational participant in that state? Conversational meaning: what conversational states are appropriate for a given word/construction and what import will that word have in such a state?