Fe-based amorphous alloys have continuously attracted extensive attention due to their excellent soft magnetic properties, such as high saturation magnetization, high permeability, low coercivity, and low core loss. However, the theoretical studies on the magnetism of amorphous alloys remain incomplete, and the structural origins of the magnetic properties in Fe-based amorphous alloys are still unclear, making it difficult to fully explain their magnetic behaviors. Existing research primarily focuses on how different elements affect the electronic structure, magnetic moment, saturation magnetization, and other properties of iron-based amorphous alloys. However, little effort has been paid to the in-depth exploration into the underlying mechanisms of the local atomic structures, including short-range and medium-range order, influence magnetic properties. This review summarizes the recent experimental and computational progress in exploring the potential correlation mechanism between amorphous structures and soft-magnetic properties, aiming to provide a reference for further elucidating the structural origins of magnetic properties in Fe-based amorphous alloys, and to identify key unresolved issues in future research.