Inspired by the belief that cognitive and pragmatic models of communication and discourse processing offer great potential for the study of Audiovisual Translation (AVT), this paper will review such models and discuss their contribution to conceptualising the three inter-related sub-processes underlying all forms of AVT: the comprehension of the multimodal discourse by the translator; the translation of selected elements of this discourse; and the comprehension of the newly formed multimodal discourse by the target audience. The focus will be on two models, Relevance Theory, which presents the most comprehensive pragmatic model of communication, and Mental Model Theory, which underlies cognitive models of discourse processing. The two approaches will be used to discuss and question common perceptions of AVT as being ‘constrained’ and ‘partial’ translation.