This article examines how addressing climate-related risks and supporting mitigation and adaptation policies fit into central bank mandates. We conduct an analysis of mandates and objectives using the IMF's Central Bank Legislation Database and compare these to sustainability-related policies central banks have adopted in practice. Out of 135 central banks, only 12% have explicit sustainability mandates, while 40% are mandated to support the government's policy priorities, which mostly include sustainability goals. However, given that climate risks can directly affect central banks' traditional core responsibilities, all institutions ought to incorporate climate-related physical and transition risks into their policy frameworks to safeguard...