Although it is increasingly recognised that higher education institutions have to play a critical role in the progression towards a sustainable development, the question of what fields and issues universities should attend to in their attempt to become more sustainable remains subject to debate. In recent years, sustainability assessment tools have begun to play a prominent role in strategies to reorient higher education institutions systematically and holistically towards sustainability. In the course of their further advancement, sustainability assessment tools have not only become instrumental facilitators of change processes towards sustainability, but also established implicit normative standards by framing the overall understanding of what fields and issues a sustainable university should engage with. So far, researchers in the field have paid little attention to the understandings of a sustainable university that are underpinning and informing sustainability assessment tools. This paper addresses this gap. Based on a comparative analysis of indicators and criteria, as well as introductory passages in supporting documents of twelve sustainability assessment tools, the authors sketch the dominance and marginalisation of different fields and issues. In doing so, the paper contributes to building the capacity for a more sophisticated and reflexive engagement with different approaches to assess and evaluate sustainability in higher education institutions.