Simultaneous interpretation (SI) is among the most complex of human cognitive/linguistic activities. This study, which will interest practitioners and trainers as well as linguists, draws more on linguistics-based theories of cognition in communication (cognitive semantics and pragmatics) than on the traditional information-processing approaches of cognitive psychology, and shows SI to be a valuable source of data on language and cognition. Starting from semantic representations of input and output in samples of professional SI from Chinese and German into English, the analysis explains the classic phenomena - anticipation, restoration of the implicit-explicit balance, and communicative re-packaging ('re-ostension') of the discourse - in terms of an intermediate cognitive model in working memory, allowing a more unitary view of resource management in the SI task. Relevance-theoretic analysis of the input discourse reveals rich pragmatic information guiding the construction of the appropriate contexts and the speaker's underlying intentionalities. The course of meaning assembly is reconstructed in annotated synchronised transcripts.