The aim of this study is to provide a systematic review of the various criticisms concerning global university rankings. To understand these criticisms, it seems essential to outline the methodology of different global rankings. Subsequently, the paper proceeds by discussing the challenges related to measuring the teaching activity, research performance and institutional reputation of HEIs, including the problems of data collection and presentation of results. The final part of the paper outlines two possible directions for the future of university rankings. It discusses the possibility of ‘fixing’ the rankings and it also examines the more radical, but increasingly widespread solution, i.e. the possibility of abandoning the ranking of HEIs altogether.