Despite the increasing relevance of cross-border flows of goods, capital and people in shaping risks and opportunities today, we still live in a “bordered” world, where the nation state plays a key role in planning and governance. Yet, climate change impacts will not be contained within country borders, meaning that climate change adaptation governance should also consider “borderless climate risks” that cascade through the international system, in relatively simple or highly complex ways. In this paper, we demonstrate how the notion of borderless climate risks challenges the dominant territorial framing of adaptation and its problem structure. To advance knowledge, we ask: why has a territorial framing and the national and sub-national scales dominated adaptation governance? How do borderless climate risks challenge this framing and what are possible governance responses? We draw on constructivist international relations theory and propose that the epistemic community that developed to interpret climate change adaptation for decision-makers had certain features (e.g. strong environmental sciences foundation, reliance on place-based case study research) that established and subsequently reinforced the territorial framing. This framing was then reinforced by an international norm that adaptation was primarily a national or local responsibility, which has paradoxically also informed calls for international responsibility for funding adaptation. We conclude by identifying types of governance responses at three different scales—national and bilateral; transnational; international and regional—and invite more systematic evaluation by the IR community.