This chapter uses an object-oriented approach to explore how the Arctic is being constituted as an object of global governance within an emerging ‘global polity’, partly through geoengineering plans and political visions ('imaginaries'). It suggests that governance objects—the socially constructed targets of political operations and contestations—are not simple ‘issues’ or ‘problems’ given to actors to deal with. Governance-objects emerge and are constructed through science, technology and politics, and rather than slotting neatly into existing structures, they have their own structuring effects on world politics. The emergence of the Arctic climate as a potential target of governance provides a case in point. The Arctic climate is becoming globalised, pushing it up the political agenda but drawing it away from its local and regional context.