Despite over 50 years of messaging about the reality of human-caused climate change, substantial portions of the population remain sceptical. Furthermore, many sceptics remain unmoved by standard science communication strategies, such as myth busting and evidence building. To understand this, we examine psychological and structural reasons why climate change misinformation is prevalent. First, we review research on motivated reasoning: how interpretations of climate science are shaped by vested interests and ideologies. Second, we examine climate scepticism as a form of political followership. Third, we examine infrastructures of disinformation: the funding, lobbying and political operatives that lend climate scepticism its power. Guiding this Review are two principles: (1) to understand scepticism, one must account for the interplay between individual psychologies and structural forces; and (2) global data are required to understand this global problem. In the spirit of optimism, we finish by describing six strategies for reducing the destructive influence of climate scepticism.