The presentation deals with the transformation of borders and border controls under conditions of globalization. It begins by asking what role borders played in the formation of the modern state. Then it turns to globalization, which has intensified cross-border activities, forcing states to combine permeability and control. It discusses three specific reactions to this challenge: increased selectivity, internationalization of border controls, and extra-territorialization of control. It will show that, on average, visa-free mobility has increased over the past 40 years, but mobility rights have been distributed more and more unequally, leading to a “global mobility divide."