The transition towards a sustainable economy is currently one of the most pressing issues for managers, stakeholders and policy makers. For the banking sector, several regulatory initiatives have been promoted by European Supervisors and Regulators, which have recognized the pivotal role of financial sector in enhancing sustainable economic development and the risks to which financial intermediaries are exposed during this transition. The main purpose of this article is to outline the key elements that are crucial for a proper integration of sustainability and ESG considerations into banks’ strategic choices, business processes and risk management framework. In particular, an analysis of the main practices, regulatory requirements and outstanding issues will be performed in order to provide an overview of the main challenges that banks need to address in order to successfully incorporate ESG risks into their business processes and risk management frameworks. In addition, given the ongoing heterogeneity in the application of such regulatory expectations, the article provides an update on the state-of-the-art by reviewing the main international research and studies on this topic and by presenting the findings of some surveys carried out by the ECB and Aifirm (Associazione italiana financial risk managers) on a sample of European and Italian banks respectively.