The EU's borderland between Finland and Russia provides a fascinating setting to study how different understandings of state and civil society meet, overlap, and fuse. Focusing on this border region, this study pits the conventional bilateral framework against the more recent EU one in depicting a cross‐border space for civic activity. It offers a critical perspective on the official European Neighbourhood and illustrates a complementary vision of a non‐territorial civic neighbourhood seeking to capture the networked and fluid topologies of contemporary cross‐border processes. The paper underlines the role of civil society in bridging the gaps created by borders, and suggests that they provide a powerful driver for maintaining neighbourly relations in a tense climate. To better understand the transnational network‐space they fashion, we must abandon the geographical idea of territorial exceptionality and be receptive to alternative interpretations not tied to a particular policy framework and the restrictions defined by it.