Climate change will not only have a major impact on people’s health, it will also affect the health systems and infrastructure that people need for their treatment. Paradoxically, though, our current health systems are a substantial contributor to greenhouse gas emissions. So what actions must be taken to tackle both problems simultaneously, protecting both human and planetary health? How do we build climate-resilient health systems, and who should pay for them? Can the lessons of Covid-19 guide and prepare us for future health crises?