This essay is about the role of visual surveillance technologies in the policing of the external borders of the European Union (EU). Based on an analysis of documents published by EU institutions and independent organizations, I argue that these technological innovations fundamentally alter the nature of national borders. I discuss how new technologies of vision are deployed to transcend the physical limits of territories. In the last twenty years, EU member states and institutions have increasingly relied on various forms of remote tracking, including the use of drones for the purposes of monitoring frontier zones. In combination with other facets of the EU border management regime (such as transnational databases and biometrics), these technologies coalesce into a system of governance that has enabled intervention into neighboring territories and territorial waters of other states to track and target migrants for interception in the “prefrontier.” For jurisdictional reasons, this practice effectively precludes the enforcement of legal human rights obligations, which European states might otherwise have with regard to these persons. This article argues that this technologically mediated expansion of vision has become a key feature of post–cold war governance of borders in Europe. The concept of transterritory is proposed to capture its effects.