For the last ten years, the notion of a green economy has become increasingly attractive to policy makers. However, green economy covers a lot of diverse concepts and its links with sustainability are not always clear. In this article, we focus on definitions of green economy and related concepts and an evaluation of these concepts against the criterion of strong and weak sustainability. The article serves three purposes: Firstly, we identify and describe diverse theories, concepts, approaches and tools related to a "green economy". Among these are the theories of environmental economics and ecological economics, the concepts and approaches of cleaner production, waste hierarchy, bio-economy, industrial ecology, circular economy, nature-based solutions, and dematerialization through product-servicizing, and tools like life cycle assessment, and cost-benefit analysis. Secondly, we develop a framework that shows the capacity of the green economy concepts, approaches and tools to support the transition towards sustainability. Such a framework can serve as a heuristic to embed diverse concepts and approaches into a green economy framework. Thirdly, we briefly discuss green economy concepts with respect to their impact on strong and weak sustainability. Depending on the different concepts, approaches and tools identified in the green economy framework, different degrees of substitutability and trade-offs between environmental and economic benefits are allowed, and more or less structural changes of our modes of living are required. By discussing the notion of green economy and related concepts, approaches and tools we seek to make a contribution to their definitions and relationships as a prerequisite for operationalizing green economy.