Global climate change is often thought of as a steady and approximately predictable physical response to increasing forcings, which then requires commensurate adaptation. But adaptation has practical, cultural and biological limits, and climate change may pose unanticipated global hazards, sudden changes or other surprises, as may societal adaptation and mitigation responses. We outline a strategy for better accommodating these challenges by making climate science more integrative, in order to identify and quantify known and novel physical risks even–or especially–when they are highly uncertain, and to explore risks and opportunities associated with mitigation and adaptation responses by engaging across disciplines. This improves the chances of anticipating potential surprises and identifying and communicating “safe landing” pathways that meet UN Sustainable Development Goals and guide humanity toward a better future.