This editorial outlines the theoretical and methodological underpinnings of the current special issue, signalling some of the practical implications of the problems investigated. As the title of the collection highlights the convergence of “translation” and “cognition”, emphasis is here first placed on what “cognitive” can be taken to stand for in translationcentred research. I then discuss the other identifying idea of the issue - that of asymmetry - i.e. the observation that conceptual-semantic content is variably partitioned as it gets coded in different languages. Special attention is paid to cross-linguistic conventionalisation misalignment which requires sensitisation to translation scenarios where the symmetry of the source and target structures is only illusory.