Central banks are faced with the financial challenge of climate change: on the one hand, the need for a massive reallocation of financial flows from “brown” to “green” activities and sectors and on the other hand climate related financial risks considered as systemic. Responding to this challenge will lead to profound changes in their doctrine and practices. This article shows that history is punctuated by such rapid changes in central banking. It analyses the arguments for integrating financial climate risks into central banks’ doctrine and operational framework and attempts to explore what a greening of central bank actions might mean in practice.