This chapter examines argumentative talk-in-interaction in video-recorded public debates held in Switzerland, during which all the participants were temporally and spatially co-present. It focuses on the issue of segmenting talk into argumentative moves, by looking at the way gestures combine with the verbal mode to enhance and display the different steps of the ongoing argumentation (e.g. when the speaker moves from one argument to another, or from an argument to the conclusion). In other words, while the embodied dimension of argumentation in talk-in-interaction remains largely unexplored, the chapter provides empirical evidence for the way argumentation is multimodally produced and processed in context. Three specific gestures are considered: gestures claiming the floor, gestures pointing to a participant, and metaphoric grasping gestures. The chapter concludes with suggestions for further lines of research.