This article explores the potential implications on financial stability of new global and systemic ecological risks (“Green Swans”), including climate-related risks and the Covid-19 pandemic. Rather than proposing a single policy tool (such as a supposedly optimal carbon tax or measurement of climate-related risks) to address extremely complex and non-linear phenomena, it explores broader analytical frameworks that can better embrace the radical uncertainty and the need for structural transformations associated with contemporary ecological risks. An unprecedented level of cooperation among multiple players, including central banks, will be required. Such cooperation raises new challenges. In particular, it requires making difficult trade-offs between the quest for more efficiency and the need for more resilience in the governance of our complex socio-ecological systems.