In the face of mounting evidence of global warming, which is an irreversible process, setting a social price of carbon at the global level and devising appropriate metrics to assess climate risks at a microeconomic level are the current priorities. Central banks, as other policymakers, have to play their part and thus consider climate risks when devising their strategies, conducting their policies and implementing their decisions. In doing so, they can rely on market forces. At this stage, this seems to require some limited adaptations of their monetary policy frameworks rather than profound changes. However, climate change risks are bound to take an increasingly important role in the conduct of financial stability policies in the coming years.