In this position paper we define an interculturally competent translator as one that demonstrates a high level of intercultural knowledge, skills, attitude and flexibility throughout his or her professional engagements. We argue that to attain this goal in translator training intercultural competence needs to be introduced into the curriculum explicitly and in a conceptually clear manner. In this article we provide an overview of earlier attempts at discussing the role of intercultural communication in translator training curricula and we discuss the various pedagogical and practical challenges involved. We also look at some future challenges, identifying increasing societal diversity as both a source of added urgency into intercultural training and a challenge for traditional biculturally based notions of translators’ intercultural competence and we argue for the central role of empathy. Finally, and importantly, we introduce the contributions to the special issue.