"Internationalisation", the growing border-crossing activities between national systems of higher education is losing ground to "globalisation", increasing border-crossing activities of blurred national systems which is often employed to depict world-wide trends and growing global competition. This article addresses recent issues of knowledge transfer. It points out tensions between increasing diversity in higher education and efforts to facilitate recognition of prior studies on student mobility. It shows the diversity of steering and management policies with respect to internationalisation and globalisation. Finally, it asks whether globalisation of higher education has to be viewed as a manifestation of "turbo-capitalism" or could be viewed instead as a move towards "global understanding".