This paper argues that the United Nations Framework Convention on Climate Change (UNFCCC) might be one of the biggest and most important global governance failures of our time. The paper asks why climate change has been such a hard problem to tackle by exploring the importance of cognition (processes of thought) for both past political conflicts and the possibility of future cooperation on climate change within the multilateral system. The paper introduces cognitive-affective mapping as a novel research tool that can facilitate a cognitive research programme by providing ‘access to the mind’. Cognitive-affective maps open up a wealth of analytical opportunities, including a comparison of individual and collective belief systems and mental structures that might inhibit cooperative outcomes at the international level. The study assesses to what extent mental content and structures influence the search for cooperative solutions and how cognitive obstacles to cooperation can be removed.