Ti-Ni-based alloys are quite attractive functional materials not only as practical shape memory alloys with high strength and ductility but also as those exhibiting unique physical properties such as pre-transformation behaviors, which are enriched by various martensitic transformations. The paper starts from phase diagram, structures of martensites, mechanisms of martensitic transformations, premartensitic behavior, mechanism of shape memory and superelastic effects etc., and covers most of the fundamental issues related with the alloys, which include not only martensitic transformations but also diffusional transformations, since the latter greatly affect the former, and are useful to improve shape memory characteristics. Thus the alloy system will serve as an excellent case study of physical metallurgy, as is the case for steels where all kinds of phase transformations are utilized to improve the physical properties. In short this review is intended to give a self-consistent and logical account of key issues on Ti-Ni based alloys from physical metallurgy viewpoint on an up-to-date basis. (C) 2004 Elsevier Ltd. All rights reserved.