Warm clouds are predominant cloud types that form precipitation as well as the important objects for weather modification operations. Mechanistic research, seeding estimation, and effect evaluation based on cloud seeding models provide a key basis and scientific guidance for weather modification operations. In numerical models for warm cloud seeding over the past half-century, this study systematically and respectively introduces and compares the development progress of various hygroscopic seeding models based on Bulk, Bin, Particle-based Lagrangian and Hybrid microphysics schemes. A comprehensive examination was provided for the application of a series of models, focusing on salt powders and flares in artificial precipitation enhancement, defogging, precipitation reduction, actual seeding effect evaluation, and mechanism research. It further summarizes the current scientific consensus and existing problems and finally looks forward to the key directions of future scientific research. This will have important guiding significance for the in-depth development of warm cloud seeding numerical models, the study of precipitation enhancement mechanisms, and the application of weather modification operations.