During the past several years many new results have been obtained for Fresnel zone plate antennas having a focal length to diameter ratio (F/D) near unity. Although zone plates have been used for many years at optical wavelengths, the typical configuration has employed F/D values from 20 to 100, sometimes greater than that. This results in a small angle (a few degrees or less) at the focal region, whereas the focal angles for F/D near unity (between 0.5 and 2.0) range from 90° to 28.1°. The small-angle optical conditions permitted making approximate analytical solutions which do not apply to the large-angle case. The recent results for large-angle applications will be summarized for microwave and millimeter-wave examples, although they are valid at any wavelength. In addition, a description will be given of optimization of feed methods (typically corrugated horn antennas) to improve overall efficiency (including aperture efficiency and diffraction efficiency), while also improving (lowering) first-sidelobe levels. This involves solving the case of tapered amplitude illumination across the zone plate aperture, whereas most of the previous investigations have assumed uniform illumination. A truncated Gaussian amplitude distribution with a 10 dB taper at the edge of the aperture provides the optimum aperture efficiency, as well as low sidelobe levels. The utilization of zone plate antennas at terahertz frequencies will also be described. At these frequencies the thin structure of the planar zone plate offers much lower loss than that of a conventional lens. All transparent materials increase in attenuation (loss tangent) as one moves from microwave frequencies to the terahertz range, and conventional lenses have high attenuation. This makes the use of the zone plate lens a preferred choice, for certain configurations.