Holograms synthesized by computer are used for constructing optical wavefronts from numerically specified objects. Elimination of the need for a physical object has made new applications possible, for example, three-dimensional computer output displays, synthetic prototypes for interferometric testing, and filters for various optical data processing operations. Our computer holograms differ from a normal hologram in that the transmittance is binary, yet they are able to construct general wavefronts and images efficiently and have several practical advantages over holograms with a continuous range of transmittance. Recent improvements that simplify the production of binary holograms and improve their performance are described and experimental work showing reconstruction of two- and three-dimensional images is presented.