Diffractive optical components were widely used in many fields such as optical sensing, optical communication, computational optics, laser beam shaping, biomedicine, and optical data storage. This paper first summarizes the development of diffractive optical elements based on scalar diffraction theory in various stages. The development of diffractive optical elements can be divided into four stages: Fresnel zone plate, hologram and kinoform, binary optical element, and diffractive optical element. The design principles, structural characteristics, processing difficulties, diffraction efficiency, and application possibilities in reality are analyzed for each stage of diffraction elements followed by an overview of diffractive optical elements based on vector diffraction theory. Finally, a summary of current applications of diffractive optical elements in conventional and new imaging and non-imaging systems is presented. The current problems in the development of diffractive optical elements are sorted out and the future development trend is predicted according to the corresponding problems, which will be a guide for the future research of diffractive optical elements.