<p>Internationalisation of the curriculum (IoC) is on the agenda of many universities worldwide, but its development is slow and fragmented. The complexities and controversies contained in the IoC concept make it difficult for faculty members to learn and relate to their teaching practices. This study aims to clarify the concept of IoC to encourage constructive discussions and move the field forward. We adopted a threshold concepts lens because threshold concepts are transformative, which can help learners acquire troublesome concepts and move to a new level of understanding. We identified 30 statements about IoC through Delphi techniques involving eight experts in three rounds. A main finding is that IoC as a whole represents a powerful threshold concept that brings a transformative lens to curriculum design. Meanwhile, the controversies around IoC, revealed through the experts’ comments, showed that the transformative potential of IoC is yet to be realised. Our findings have implications for the future development of IoC regarding realising its transformative potential, possibly through acknowledging and addressing the discrepancies between the ideal and the reality, recognising the power differentials and biases embedded in the curriculum, and striving towards equality and diversity.</p>