The diagnosis and treatment of malocclusion, and the proper design of restorations and prostheses, requires the determination of surface topography of the teeth and related oral structures. Surface contour measurements involve not only affected teeth, but adjacent and opposing surface contours composing a complexly interacting occlusal system. No a priori knowledge is predictable as dental structures are largely asymmetrical, non-repetitive, and non-uniform curvatures in 3-D space. Present diagnosis, treatment planning, and fabrication relies entirely on the generation of physical replicas during each stage of treatment. Fabrication is limited to materials that lend themselves to casting or coating, and to hand fitting and finishing. Inspection is primarily by vision and patient perceptual feedback. Production methods are time-consuming. Prostheses are entirely custom designed by manual methods, require costly skilled technical labor, and do not lend themselves to centralization. The potential improvement in diagnostic techniques, improved patient care, increased productivity, and cost-savings in material and man-hours that could result, if rapid and accurate remote measurement and numerical (automated) fabrication methods were devised, would be significant. The unique problems of mapping oral structures, and specific limitations in materials and methods, are reviewed.