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, we derive a set of important criteria to ensure that climate risk tools provide high quality, comparable, and decisionrelevant results. We then use a sample of 16 climate transition risk tools and conduct two lines of research: First, by aid of descriptive analysis, we assess the tools' coverage of risk sources and financial assets, their inputs (i.e. underlying climate scenarios), and their outputs (i.e. climateadjusted financial metrics). Second, we use 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 our descriptive and criteria-based analysis, we derive 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.