Higher education institutions have an unavoidable responsibility to address the looming economic, environmental and social crises imperilling humans and ecosystems by placing "education for sustainability" at the heart of their concerns. Yet, for over three decades, the practice of 'higher education for sustainability' (HEfS) has encountered significant barriers to implementation, begging the question as to why. Drawing on a diverse, interdisciplinary literature, we identify four structural impediments to implementing HEfS: (1) disciplinary contestation, which creates confusion over what "sustainability" means; (2) institutional fragmentation, which prevents the interdisciplinary dialogue that sustainability demands; (3) economic globalisation, which transforms higher education into just another market opportunity; and (4) "fast and frugal" habits of reasoning, which steer time-pressed academics towards poorly integrated decisions and unsustainable positions. Our analysis highlights that wider structural change within and beyond the academy will be required if higher education institutions are to meet their responsibilities and drive the necessary social transformation.