While state borders remain the pre-eminent frontiers within geopolitics, regional blocs are also acquiring frontier characteristics. How might we understand the function and identity of such frontiers? Taking the European Union as its focus, this article offers answers to these questions by developing the idea of geostrategy. Four geostrategies are identified: networked (non)borders, march, colonial frontiers and limes. Each corresponds with a particular way of territorialising the space of the border, as well as a certain idea of 'inside' and 'outside', and of the risks and problems that the border is to govern. A geostrategic perspective uses contemporary social forms (such as networks) but also historical forms of borders (march, limes) in order to enhance the intelligibility of the frontiers of the EU. As such, this approach seeks to capture the multiplicity and plurality of borders.