Methods for grinding and polishing IR transmitting materials are described and contrasted with better known methods for making glass optics. Because many IR optical systems use aspheric surfaces, single-point diamond turning (SPDT) is suggested as the most prudent method of making both reflective and refractive aspheric surfaces. For cases in which sufficiently good surface finish cannot be achieved with SPDT, either for system use or for testing with visible-light test equipment, a postpolishing technique that uses fine diamond paste and synthetic polishing pads is given as an alternative method. Finally, some practical aspects of good mechanical and optical engineering relating to SPDT are reviewed. By taking a few simple precautions and by building in appropriate optical alignment and mechanical mating surfaces, a difficult test and assembly situation can be reduced to something that is trivial.