Computer holography is a subject of interest to a small but increasing number of researchers. This paper briefly describes the concept and history of computer holography, how it works, and its possible applications. Also presented are the recent approaches to computer holography developed at Stanford University, and a procedure for synthesizing this new class of computer holograms. These new on-axis holograms are very efficient both in their use of reconstruction light and in their use of display resolution elements during synthesis. They keep the advantages of the kinoform, a previous approach by IBM, but do not have its limitations. One approach makes use of color reversal film, such as Kodachrome II. Another approach only requires phase-transmittance material, but preserves both amplitude and phase information. Experimental results are presented.