Unlike conventional finance, sustainable finance seeks to integrate social, environmental, and climate change considerations into financial institutions’ business strategies. The financial system’s ability to positively respond to sustainability transition demands is contingent upon a directional transformation that involves regulatory, political, structural, theoretical, and relational shifts. Accordingly, this paper performs a quali-quantitative analysis that combines both a bibliometric method with a content analysis process to investigate the trend of sustainable finance literature in the Scopus database and provide directions for potential future research. Our bibliometric performance analysis of 723 publications reveals that the UK, China, the US, Switzerland, and Japan are the major centers of research excellence in sustainable finance. They are the most productive countries and hold the most relevant institutions. Moreover, the prevalence of transdisciplinary journals over mainstream finance and economics sources is obvious. Our network map analysis, on the other hand, shows the substantial relevancy of sustainable/green banks’ involvement in sustainable development. Nonetheless, its relatively low density underlines the existence of relevant research gaps. Therefore, we undertake a content analysis of that particular topic’s literature to derive its conceptual structure and truly understand banks’ important role in sustainability transition. Key research themes in this respect include sustainability performance and banks’ profitability associations; sustainable banks’ risk profile; determinants of banks’ willingness to introduce sustainability criteria into their business strategy; depositors’/customers’ responsiveness to banks’ sustainability performance; and relevant macroprudential regulations, monetary policies, and supervisory guidelines to sustainability transition.