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Climate mitigation scenarios are an essential tool for analyzing the macroeconomic and financial implications of climate change (physical risk), and how the transition to a low-carbon economy could unfold (transition risk). The Network for Greening the Financial System (NGFS) has co-developed a set of climate mitigation scenarios for climate financial risk assessment. Despite the important role that these scenarios play in climate stress tests, the understanding of their main characteristics and limitations is still poor. In this paper, we contribute to filling this gap by focusing on the following issues: comparison of the process-based Integrated Assessment Models (IAMs) used by the NGFS with alternative models; the role of Representative Concentration Pathways (RCPs) and Shared Socioeconomic Pathways (SSPs) in shaping the scenario narratives, and their shortcomings; the interpretation and sensitivities of carbon price pathways; and, comparison with other climate mitigation scenarios. We then draw lessons on how to increase the relevance of the NGFS scenarios. These include updating the SSP narratives; considering the potential trade-offs between different types of climate policies; assessing acute physical risks and their compounding; integrating physical risks within transition scenarios; and, taking into account the role of the financial sector and investors’ expectations.