Financial meteorology is an innovative interdisciplinary science that combines meteorological sciences and technologies with economic and financial theories, focusing on the needs of financial institutions or to help meteorologically sensitive industries such as agriculture, energy, transportation, electricity and tourism to manage their meteorological risks. Financial meteorology involves research in areas of financial meteorological indices, weather derivatives (financial derivates based on meteorological indices), meteorological risk assessment and forecasting, and meteorological risk management, which characterizes the meteorological risk exposure of economic entities. This paper systematically reviews the impact of meteorological risks on the financial sectors, summarizing key developments and domestic and international practices in meteorological services for insurance, bank, securities and related sectors. These include meteorological index insurance, meteorological risk stress testing, and weather derivatives. The study further highlights recent progress in the development of financial meteorology in China, such as policy support, the establishment of the China Financial Meteorological Index and Service Platform (CFMis), and enhanced collaboration with financial institutions. The next step of financial meteorology will primarily focus on advancing the research and development of financial meteorological theories and products, constructing large-scale financial meteorological models, promoting trading of weather derivatives, refining financial meteorological standards and regulatory frameworks, and fostering interdisciplinary talents. These efforts will enhance the capacity of financial institutions to manage meteorological risks and contribute to the high-quality development of finance.