Current optical finishing technology limits the choices for synchrotron radiation materials to a relatively few materials: fused silica and ULE(TM), silicon CVD silicon CVD silicon carbide, and electroless nickel. We review, in a general way, those materials and several others that can be finished to the required figure and finish levels, generally considered to be < 3 microradians rms and < 5 Angstrom rms. With the objective of material choices for synchrotron beam line mirrors in mind, we briefly discuss dimensional stability, cooling, bending, polishing, and manufacturing procedures. After discussing specific materials: those previously mentioned and aluminum, Glidcop(TM), invars, and steels, we conclude that metals are best from an engineering and cost standpoint, but ceramics, including silicon me best from a polishing standpoint.