This paper elaborates a typology of universities in which each university is characteristically associated with (i) diverse missions, (ii) different ways of producing knowledge and (iii) contrasting pedagogical configurations. Four university forms are identified, analysed and illustrated, namely the expert university, the non-elite university, the entrepreneurial university and the revolutionary university. It is suggested that the typology and the analysis of university forms offered here provide insight into the current positioning of universities in relation to the wider world and have potential in prompting new forms of university for the twenty-first century. The paper further advances another possible university for the future, namely "the complex university." The complex university is part of and respectful of diverse ecosystems. It creates new frameworks to understand the world and, in that way, supports social transformations.