Abstract: Computational highlight holography converts three-dimensional computer models into mechanical "holograms" fabricated on (specular) reflective or refractive materials. The surface consists of small grooves with patches of paraboloids or hyperboloids, each of which produces a highlight when illuminated by a directional light. Each highlight appears in different places for different view directions, with the correct binocular and motion parallax corresponding to a virtual 3D point position. Our computational pipeline begins with a 3D model and desired view position, samples the model to generate points that depict its features accurately, and computes a maximal set of non-overlapping patches to be embedded in the surface. We provide a preview of the hologram for the user, then fabricate the surface using a computer-controlled engraving machine. We show a variety of different fabricated holograms: reflective, transmissive, and holograms with color and proper shading. We also present extensions to stationary and animated 2D stippled images.