Theory and experiments in the area of computer-generated holograms for geometric transformations are presented. Geometric transform holograms are divided into two categories: (1) those which have a continuous fringe structure and (2) those which consist of a set of discrete subholograms. Criteria for the realizability of a continuous geometric transform hologram are described. Examples of both types of holograms are developed to map rings of different radii to a linear sequence of points. They allow the replacement of a ring detector by a linear detector array without loss of signal energy and can be applied to optical spectrum analysis and angle-wavelength multiplexing for data transmission through optical fibers.