First published online: 25 May 2017This introduction provides a descriptive typology and normative analysis of the ways boundaries are being questioned in Europe. We distinguish between boundary-making (defining or redefining the territorial borders of a polity), boundary-crossing (determining the rules of access to territorial borders) and boundary-unbundling (allowing boundary-making and boundary-crossing to vary between policies and polities), noting each of these categories possesses internal and external dimensions. Cosmopolitans and statists offer contrasting normative evaluations of these processes, favouring weakening and maintaining or strengthening state boundaries respectively. We endorse a democratic approach lying between these...