University campuses are increasingly diverse, reflecting substantial growth in student enrolments, but this has not translated to equitable outcomes for all students. While much attention has been focused on student retention and success, particularly for those from non-traditional backgrounds, dominant theoretical models rest on a limited notion of cultural capital that places undue responsibility on students themselves. We suggest that structural inequality, whereby some people receive unequal privileges and opportunities, offers a more productive, less problematic framework for use by academic staff, university leaders and policy makers to address these challenges. In this article, we identify three types of structural inequality -- vertical, horizontal, and internal -- and include a taxonomy of internal inequalities to prompt further research and policy outcomes. Put simply, rather than ask how students can build cultural capital to assimilate to their institutions, we should ask what institutions can do to include students, staff, and the wider community.