Amorphous alloy is a kind of metallic materials prepared by rapidly cooling the alloy melt through hindering crystallization in cooling process. Due to the unique structure of atomic random packing, Fe-based amorphous alloys exhibit not only structural and property isotropy, but also small structural correlation length, small magnetic anisotropic constant, and then small coercivity Hc. Like crystalline Fe-based alloys, Fe-based amorphous alloys also possess high saturation induction Bs. As a result, research on engineering applications of Fe-based amorphous alloys has been promoted by their excellent soft magnetic properties. Now Fe-based soft magnetic amorphous/nanocrystalline alloys have been produced and applied to various areas on a large scale. Here in this paper, the processes of discovery, development and application of Fe-based soft magnetic amorphous alloys are reviewed, and the effects of chemical composition, structure and preparation technology on the soft magnetic properties are introduced and discussed. The obtained theoretic results and the technological innovation show that the great contributions have been made to the development and application of Fe-based soft magnetic amorphous/crystalline alloys. Based on the progress of structure and soft magnetic property and our understanding, the development process of the fundamental research and the application progress of Fe-based soft magnetic amorphous alloys could be divided into three periods. In addition, the present challenge topics in their researches and applications are proposed.