We investigate the notions of continuity and interaction in linguistic models. There is now a quite rich tradition of work based on the hypothesis that natural language is not a discrete model. Instead, continuous models consider word sense, grammar rules and categories as continuous notions: some words are hard to categorize and some rules do not fully apply in certain contexts. Word meaning in context often corresponds to different meanings according to the dictionary. New models have been proposed that provide a more accurate view of these phenomena. Recent advances in natural language processing also support this idea by providing very rich models based on a multi-level representation of the context of use of linguistic items. We describe how these models provide an interesting convergence between linguistic and computational models.