Purpose: This viewpoint paper addresses the use of sustainability frameworks in embedding education for sustainability into the curriculum of higher education institutions (HEIs). The purpose of this paper is to explore the paradox that sustainability frameworks must facilitate transformation of existing structures whilst also being well-enough aligned with current conditions to be readily adopted by today's HEIs. Design/methodology/approach: This paper proposes a set of four criteria for assessing the suitability of sustainability frameworks for use across the curriculum: relevance to current curricula, language, institutional fit and concept of the future. Using these criteria, this paper assesses how various frameworks align with the current (unsustainable) state of affairs and their transformative potential. The frameworks assessed are: the sustainable development goals (SDGs), the three pillars framework and the capitals approach. Findings: This paper finds that each of the frameworks has strengths and weaknesses: the SDGs and the capitals approach perform well on alignment but less well on transformational criteria. Conversely, the three pillars framework performs well on transformation criteria but less well on alignment criteria. By applying the criteria set out in this paper, the authors hope those working to embed sustainability into the curricula of HEIs will be better equipped to navigate the tensions presented by sustainability transitions. Originality/value: Using a novel set of criteria for assessing sustainability frameworks, this paper provides guidance that was previously lacking in education for sustainability professionals who are attempting to embed sustainability into the curriculum at HEIs.