The discussion about universities' potential to play a major role in the transformation towards a sustainable society is ongoing and often controversial. This is due to different perceptions of the role of the university and its contributions to society. For this reason, a review has been carried out into theoretical approaches that frame the relationship between university and society. After a systematization and short introduction of the different approaches, we look at their common architecture in order to derive key elements that have to be taken into account if a university wants to (re-)define its relationship with society. We describe different forms of a transformative university through the lens of each approach and we highlight conflicts that might arise in comparison with the traditional idea of a university. We conclude by breaking down the results of our analysis into three questions for universities wanting to become a transformative force for a sustainable society.