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. These poorly known factors could substantially affect the urgency of mitigation as well as adaptation decisions. 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 including those arising from interactions with ecosystems and society. We need to do this even–or especially–when they are highly uncertain, and to explore risks and opportunities associated with mitigation and adaptation responses by engaging across disciplines. We argue that upcoming climate assessments need to be more risk‐aware, and suggest ways of achieving this. These strategies improve 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.