Most thinking about the relations between states is stuck in an orderly perception of reality. The objective of theory and practice is commonly to create order out of the ever-changing natural disorder of self-interested states competing in a self-organised system. After summarising this thinking and the salient literature this chapter outlines the complexity thinking version of global politics which more accurately reflects the dynamic nature of global reality. Depending on the issue-area this may require accepting an ontology of global politics that privileges processes over entities and the rules of interaction over the characteristic of states and organizations that is notably the case in global environmental issues. The chapter then applies this process-based complexity thinking to the global climate issue, demonstrating that the approach is readily applicable and produces a more reasonable description of reality and a better explanation for the failure of states to agree on an effective mitigation strategy. However, the emergent scientific consensus has been an effective stimulant to action at lower scales. This section is followed by a short conclusion.