Key Messages: i) Adaptation science should support the policy community to adopt a transboundary lens to better manage the systemic nature of climate risk. ii) Adaptation is not (just) local or national – it can also be regional or global, it requires scientific knowledge and cooperation at all scales, and should be recognized as delivering, in some cases, global public goods. iii) Adaptation is not necessarily benign – it can redistribute vulnerability and create or magnify risk for others, especially across borders. iv) Adapting to transboundary climate risk falls between the remits of government departments and national jurisdictions and ends up being “no-one’s job” – analysis is needed to support solutions at various scales.