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Climate-related financial risks might have the potential to trigger the next systemic financial crisis, as recently stated by the Bank of International Settlements. In consequence, understanding these so-called Green Swan risks should be a key priority in financial decision making and supervision. However, a systematic approach and a comprehensive theory on climate-adjusted financial risk metrics is still missing. This study is a first step to fill this gap, with a focus on transition risks. Drawing on insights from climate science, economics and finance research, this paper derives a set of important criteria to ensure that climate risk tools provide high quality, comparable, and decision-relevant results. A sample of 16 climate transition risk tools are used to conduct two lines of research: First, by aid of descriptive analysis, the paper assesses the tools’ coverage of risk sources and financial assets, their inputs (i.e. underlying climate scenarios), and their outputs (i.e. climate-adjusted financial metrics). Second, the paper uses the previously defined criteria for an in-depth analysis of the quality, comparability and decision-relevance of the tools. The results will be presented at the individual tool level, and at the meta level. Based on the results of this descriptive and criteria-based analysis, the paper derives potential next steps for tool provider, conclusions for potential tool users, and guidelines for supervisory authorities. The analysis could be used as starting point for building a comprehensive theory of meaningful climate-related financial risk indicators, aid practitioners to select the tools best suited to their needs and use cases, and inform regulatory processes on financial climate risk assessment principles.