The medium we use to communicate (oral, written, or even gestural) plays an important role in the way we structure and organize our discourse. To do this, we can draw on linguistic markers, such as connectives, discourse markers or frame markers, or on (marked) information structure constructions. What is the impact of the nature of the medium (spoken vs. written vs. gestural) and of the style of the discourse at hand (formal vs. informal) on the choice of one linguistic expression over the other? While medium seems to play a role in the discrimination between text types (e.g., casual coffee conversation between colleagues, business meeting, e-novel), it is less clear what the potential impact is of extra-linguistic parameters, such as emotional weight or spatiotemporal distance between the interlocutors, on the structuring of those texts. These questions bring us face to face with the limits of the traditional dichotomic representation opposing speech and writing on the sole basis of the medium at hand. The contributions in this volume follow the suggestion to consider discourse structure not only from the perspective of variation between the written and the spoken mode, but also from the perspective of variation on a continuum from formal to informal ways of communicating.