The aim of this article is to survey and interrogate the university sector of the world ranked by international rankings critically as to the sector's pursuit of the sustainable development goals. Universities have a unique and indispensable role to play in the pursuit of the lofty objective of the sustainable development goals. However, when dealing with the global impact rankings, three provisos should be kept in mind, namely that academic autonomy is a prerequisite for a university and cannot be sacrificed, the sustainable development goals do not capture the entire round of challenges facing humanity and social metrics should be treated with circumspection, as these too have their shortcomings. Most universities, with the possible exception of a few very top-tier universities, seem not to be geared to make their contribution to the realisation of the sustainable development goals. However, pockets of excellence exist, also in the Global South, and in terms of internationalisation and comparative international studies, these should be capitalised on.