Geographers tend to see energy systems as intricately interwoven with society and relatively resistant to change. We argue that there is a danger of exaggerating the permanence and stability of the energy–society relationship. Therefore we propose a framework that is more open to instability and transformation. Using assemblage theory, we frame the social and material landscapes of oil – carbonscapes – as having emergent capacities for change built into their relations of exteriority. We illustrate this by discussing instabilities at particular points within the global oil production network: extractive hot zones, energy distribution infrastructures, and urban spaces of consumption and practice.