Translation Studies (TS) has undergone a number of internal shifts. These have focused on so-called "travelling concepts", such as 'culture' or 'cognition', and have been crucial in building and establishing the discipline. Both the concept of 'paradigm (change)' and that of 'turn' are used to refer to these shifts and frequently the two concepts are used synonymously. This essay will show why the notion of turn should be given preference over that of paradigm. The turns of TS are based on interdisciplinarity. Yet while the field has imported massively from other disciplines it has hardly exported anything. There is one exception to this trend: TS's fundamental concept, translation, is experiencing a real boom outside the discipline. However, this is happening mostly without the participation of TS itself, which has so far been both passive and ignored. It is time for TS to perform two decisive outward turns. The first must take place in order to counteract misconceived notions about 'translation proper' and about TS as a research field held by other disciplines. The second outward turn needs to be enacted in order to counteract misconceived notions about translation and interpreting generated and disseminated by translation practice. The article discusses how and why this double turn from 'inward' to 'outward' should be performed.