Topics associated with the fabrication and applications of holographic optical elements are reviewed. The existing optical elements do not always satisfy the requirements of coherent optics. The properties and applications of holographic zone plates, which act as hologram lenses, are considered. These hologram lenses can be used in holographic multiple imaging systems. Holographic diffraction gratings and some systems in which they are employed are described. Holographic elements used without additional optical parts, i.e., systems demonstrating most clearly the advantages of holographic elements, are discussed. Complex holographic systems performing functions outside the bounds of classical optics are considered.