Three-phase fluid flow in reservoirs is present in the entire process of oil field development, and three-phase relative permeability data are crucial for reservoir engineering and numerical simulation. At the same time, carbon dioxide flooding and storage have garnered significant attention recently. The calculation of dynamic storage volumes and an in-depth understanding of three-phase flow within formations are inextricably linked to three-phase relative permeability. This review is centered around the available experimental measurements, theoretical models that predict three-phase relative permeability using two-phase data, and four Lattice Boltzmann method models. By analyzing the strengths, weaknesses and limitations of each method and assessing the impact of factors like saturation history, interfacial tension, rock properties, and fluid characteristics on three-phase relative permeability, this paper seeks to offer a comprehensive understanding of the topic. In summary, we provide a concise overview of the prospects and challenges in advancing three-phase relative permeability, serving as a valuable reference for the field of carbon dioxide flooding and storage.