The European Union influences the governance of the Arctic and the Antarctic, whose Global Spaces constitute a part of broader complex governance patchworks. This influence derives both from the EU’s role in global governance but also builds on some member states being Arctic states and Antarctic Treaty parties. The objective of this article is to propose an innovative conceptual approach – built on political geography and critical geopolitics – to better capture the EU’s presence and its visions for an EU-preferred shape of polar governance. We propose that the EU is an important participant to the process of ‘polar spatial ordering’ and has its own set of objectives, namely, to establish permanent EU-polar linkages and render itself a necessary element/participant of polar (geo)politics. These aims are supported or pursued via diverse geo-policies. However, the EU’s overarching visions – cross-sectoral geo-strategies – regarding its preferred shape of polar spaces remain underdeveloped.