A well-designed phase correcting Fresnel zone plate antenna can provide performance superior to a lens or, in some cases, a paraboloid antenna, particularly at millimeter wavelengths. This paper discusses design considerations and includes approaches to give improved characteristics, such as greater efficiency or higher gain. The approaches include the use of quarter-wave or better correction, thickness designs that permit the central zone and other zones to be air dielectric (for lower losses), and the use oflow dielectric constant materials to reduce surface reflections and multiple reflections. At higher millimeter-wave or sub-millimeter wavelengths low loss materials are important. More sophisticated zoning is described, as well as the use of a compromise thickness to compensate for the fact that refraction ofwaves at the surfaces causes the path lengths through the zone plate to be different at different angles of incidence. Multiple-band zone plates are discussed.