The early 21st century is a time of great discontinuity, perhaps a tipping point in the evolving history of capitalism as neoliberalism comes under increasing criticism for its failure to manage a complex set of interlocking social, economic and environmental problems that are amplified by globalism. Higher education (HE) is more a reflection than a shaper of society. Continuing massification and the worldwide explosion of institutional and student numbers push universities into becoming enterprises. HE systems and HE Institutions (HEIs) are transforming. Are the values underpinning culture and society itself a defining characteristic of universities as ideal-seeking systems? Or do values give way entirely to business enterprise, and the triumph of neo-liberalism and market forces over public good? Are universities good for educating, informing and leading societies out of a dangerous morass? Or are they just good at being businesses trading in a free-market world? This paper takes examples of discontinuity in asking whether dichotomous tensions pulling universities in different directions can be managed; and what 21st century mission universities might usefully and successfully enact.