I have done joint work with Matthew Stone on developing a formal semantic model of the spontaneous and improvised hand gestures that happen in face to face conversation. Our model proposes a way to capture the abstract and very incomplete meanings of the gestures that are derivable from just their form, and using SDRT it also specifies in a logically precise manner how those underspecified meanings are resolved to specific interpretations via contextual information, including in particular the content of the synchronous speech. Our aim with this work is to demonstrate that the methodologies that have already been established for studying the pragmatic interpretation of purely linguistic discourse apply also to gesture, providing a seamless integration of communicative actions with both speech and gesture. In collaboration with Katya Saint-Amande (née Alahverdzhieva), I have also developed a model of how the interpretation of gesture is constrained by its form, its relative timing to speech phrases, and the form of those phrases. This form-meaning mapping is encoded in an HPSG, implemented within the Delphin Framework.