Topological photonic state, as a new type of waveguide state with one-way transport, can resist backscattering and is immune to obstacles and defects. Thus, it has found extensive potential applications in topological lasers, quantum information, optical hybrid integrated circuits, nonlinear optics, and other fields owing to its unique properties. In addition, magneto-optical photonic crystal provides an important platform for realizing topological photonic states and exploring their novel physical properties. In this paper, around the progress of topological photonic states in magneto-optic photonic crystals, firstly, we reviewed the topological photonic states in ordered and disordered lattices and revealed the microscopic physical images of topological photonic states. Next, we discussed the topological photonic states in magneto-optical photonic crystals with broken time-reversal and space-reversal symmetries and described the generation of antichiral topological photonic states. Then, we summarized the research on broadband topological photonic states and topological slow-light states and introduced novel topological optical phenomena and device design. Finally, we analyzed the key issues and prospected the future development trends in the study of topological photonic states in magneto-optical photonic crystals.