Purpose: To combat climate change and safeguard a liveable future, humanity needs fundamental and rapid social change. The purpose of this paper is to show, why and how climate communication can play an important role to nurture the public engagement needed for this change, and to explore, what higher education for sustainability can learn from climate communication. Design/methodology/approach: The scientific evidence base on climate communication for effective public engagement is summarised into 10 key principles, including "basing communication on people's values", "conscious use of framing" and "turning concern into action". Based on the author's perspective and experience in the university context, implications are explored for sustainability in higher education. Findings: The study provides suggestions for teaching (e.g. complement information with consistent behaviour by the lecturer, integrate local stories and provide students with basic skills to communicate climate effectively), for research (e.g. make teaching for effective engagement the subject of applied research), for universities' third mission to contribute to sustainable development in the society (e.g. provide climate communication trainings to empower local stakeholders) and greening the campus (develop a proper engagement infrastructure, e.g. by a university storytelling exchange on climate action). Originality/value: The study provides an up-to-date overview of climate communication research, which is in itself original. This evidence base holds interesting learnings for institutions of higher education, and the link between climate communication and universities has so far not been explored comprehensively.