Public service interpreting and translation (PSIT) is helping societies deal with the challenges posed by migration. Its consolidation as a professional practice is still a controversial subject. A number of advances can be identified across territories and settings, including the use of English when providing interpreting and translation services in lesserused language contexts, the increasing availability of training courses for public service interpreters and translators, the modest development of trainer training courses, or the rising awareness among stakeholders of the importance of relying on competent professionals when communicating with individuals who are less than proficient in the contact language or languages. However, these vital improvements are only visible in some instances and institutions in certain countries. In others, conditions in PSIT practice are far from professional. Education and training are fundamental tools for raising the status of PSIT. In this paper we take stock of experience accrued by PSIT researchers, practitioners and trainers to highlight challenges and advances in the area of PSIT training in tertiary education. After identifying successful initiatives, we single out underexplored areas, including the missing focus on translation in both training programmes and research agenda