The Communicating Climate Risk toolkit is the result of interdisciplinary collaboration across the physical sciences, social sciences, and arts and humanities, incorporating input from policy and other stakeholders. It identifies key challenges in communicating climate science, both to support robust decision-making, and to inform wider societal shifts using effective climate storytelling. It offers lessons, recommendations, and tools to address these challenges. Topics covered include varying conceptions of uncertainty and risk, best practice in visualising uncertainty data, and constructive critique of AR6 WG1 SPM methodologies for communicating model uncertainty.