In recent years, green finance has emerged as a commonly used strategy for dealing with environmental problems. However, it still remains to be seen whether green finance deals effectively with current global environmental problems. More recently, proposals regarding greening monetary policy have emerged. The goal of this paper is to provide a conceptual framework that helps to distinguish between different forms of green finance and monetary policy. We systematically analyse forms, tools and measures of green finance and monetary policy against different theoretical backgrounds. In so doing, we fill a research gap by providing an appropriate classification that is intended to facilitate future academic research. We provide different categories and distinguish, on an abstract level, between neoliberal, reformist and progressive forms of green finance. Furthermore, we provide sub-categories on a more concrete level of abstraction. With this, we focus on both financial market regulation and monetary policy strategies. Against the background of our categorisation, the different focuses on green finance and green monetary policy and the (often implicitly) underlying theoretical assumptions become transparent. The classification has significant implications for the evaluation of different perspectives and is, therefore, important for academic debate. The classification also potentially represents a basis for policy related discussions. We conclude that neoliberal forms of green finance and monetary policy that rely on the assumption of the effectiveness of markets for contributing to sustainability tend to neglect or abstract from potentially adverse distributional effects. Reformist forms of green finance and monetary policy are more skeptical of the effectiveness of market processes and, therefore, consider a greater role for government policies. In addition, reformist approaches are more concerned about the potentially adverse distributional effects of environmental policies. Finally, progressive green finance and monetary policy adopts a more global perspective on environmental issues and links the discussion intrinsically with questions of global inequality and socio-ecological transformation. Moreover, progressive approaches are skeptical of global capitalism at a systemic level and therefore demand global rules and financial and monetary regimes that allow for solutions of environmental problems based on global solidarity and a democratic economic governance.