Climate change is a particularly good example of an issue for which the definition of problems, and attempts to resolve them, contain key roles for scientific research, alongside institutions, ideology, and individual beliefs. This can lead to rich empirical questions as to the relative balance of these influences. However, the most visible discussion about the role of scientific knowledge is often a heated and simplistic debate about the details of the science itself. Post-normal science (PNS) is one way to think about the role of science and expertise more generally in addressing problems like climate change. PNS, it is argued, by extending the group of actors feeding expertise of different types into knowledge-making and decision processes, can provide a richer and more in-depth perspective and an extended function of quality control over the process of inquiry. This review introduces the concept of PNS, and some of the responses to it from various quarters. These responses offer valuable insights into the way that scientific expertise is perceived, such as perceptions about why science is used and what science should do, focusing in particular on ‘climate science-sceptic' debates. By introducing insights from science studies, political science, policy analysis, and human geography alongside PNS, the paper offers potential ways out of such debates, and also ways that PNS may develop in the future.