There is perhaps no single phenomenon connected with the metallography of the corrosion- and heat-resistant iron-chromium and iron-chromium-nickel alloys that has excited more interest on the part of investigators during the past five years than the sigma phase. The studies, as shown by the papers presented in the present Symposium, have brought into play all the methods available to the physicist and metallurgist aimed at determining what it is, under what conditions of composition, temperature and time it may form, how it forms and decomposes, how its presence may be detected and what its effects on the physical, chemical, and mechanical properties of the metal may be. The sigma phase may be described physically as a very hard, non-magnetic, brittle phase giving the X-ray diffraction pattern characteristic of the 50-50 atomic per cent iron-chromium alloy (FeCr). A tetragonal crystal structure with about 30 atoms per unit cell has been suggested as a possible structure by Duwez and Baen and by Menezes, Roros, and Read. More recent work of Pietrokowsky and Duwez indicates an orthorhombic unit cell of about 24 atoms. The tendency of binary systems to form the sigma phase appears to be governed, according to Duwez and Baen, by an agreement within 8 per cent in the atomic diameters of the reacting atoms with one of the elements having a body-centered and the other a face-centered cubic crystalline habit. Though not always designated sigma, the phase found in the Fe-Cr system is also identified in the binary systems Fe-V, Cr-Co, Co-V and Ni-V and in ternary systems based on these binary systems. Malcolm and Low and also Binder call attention to a phase they find present in certain types of 18-8 stainless steel, closely related but not identical with sigma. These investigators and also W. D. Forgeng reported this same phase, which they call X-phase, present in the X-ray diffraction patterns obtained from molybdenum-bearing 18-8 stainless steels in connection with the unpublished results of work done in collaboration with Subcommittee VI on metallography of ASTM Committee A-10 on Iron-Chromium Iron-Chromium Nickel, and Related Alloys. With a few exceptions the papers in this Symposium discuss the occurrence of sigma in the commercial types of iron-chromium and iron-chromium-nickel alloys in which it appears as a relatively low-temperature transformation product of a phase stable at higher temperatures. There is strong evidence that it forms not only by transformation of the body-centered alpha of the two phase ferrite-austenite alloys but also by direct transformation of the face-centered cubic austenite of the single phase Fe-Cr-Ni alloys. In the latter case the reverse transformation, from sigma back to austenite upon heating to high temperatures, is shown by Dulis and Smith to take place through an intermediate, quite temporary, transformation to alpha. The precipitation of carbides is observed to precede the formation of sigma and one notes an association, sufficiently frequent, of sigma and carbides to suggest the influence of one on the formation of the other. A micro-constituent having the appearance of a single phase, cursorily assumed to be carbide, is often found to be partly carbide and partly sigma after suitable etching.