A major challenge facing climate scientists is explaining to non-specialists the risks and uncertainties surrounding potential changes over the coming years, decades and centuries. Although there are many guidelines for climate communication, there is little empirical evidence of their efficacy, whether for dispassionately explaining the science or for persuading people to act in more sustainable ways. Moreover, climate communication faces new challenges as assessments of climate-related changes confront uncertainty more explicitly and adopt risk-based approaches to evaluating impacts. Given its critical importance, public understanding of climate science deserves the strongest possible communications science to convey the practical implications of large, complex, uncertain physical, biological and social processes. Here, we identify the communications science that is needed to meet this challenge and the ambitious, interdisciplinary initiative that its effective application to climate science requires.