Underlying sociopolitical factors have emerged as important determinants of wildlife population trends and the effectiveness of conservation action. Despite mounting research into the impacts of climate change on nature, there has been little consideration of the human context in which these impacts occur, particularly at the global scale. We investigate this in two ways. First, by modeling the climatic niches of terrestrial mammals and birds globally, we show that projected species loss under climate change is greatest in countries with weaker governance and lower Gross Domestic Product, with loss of mammal species projected to be greater in countries with lower CO2 emissions. Therefore, climate change impacts on species may be disproportionately significant in countries with lower capacity for effective conservation and lower greenhouse gas emissions, raising important questions of international justice. Second, we consider the redistribution of species in the context of political boundaries since the global importance of transboundary conservation under climate change is poorly understood. Under a high-emissions scenario, we find that 35% of mammals and 29% of birds are projected to have over half of their 2070 climatic niche in countries in which they are not currently found. We map these transboundary range shifts globally, identifying borders across which international coordination might most benefit conservation and where physical border barriers, such as walls and fences, maybe an overlooked obstacle to climate adaptation. Our work highlights the importance of sociopolitical context and the utility of a supranational perspective for 21st-century nature conservation.