In the present paper, the important developments on martensitic transformations in non-ferrous shape memory alloys within nearly 10 years are critically reviewed. Since the alloys include not only noble-metal alloys but also Ti-Ni based alloys, the field is very wide both in contents and in the kind of alloys. We tried to describe items with uniformity, which are common to all alloys, but specific items were also discussed when they are important. Special attention was paid to similarity and dissimilarity among alloys to highlight key points on the issues concerned. The topics include the following: (1) phase diagrams, (2) crystal structures of martensites, (3) crystallography of martensitic transformations, (4) R-phase transformation, (5) pre-transformation phenomena and origin of martensitic transformation, (6) martensite aging and rubber-like behavior, (7) martensite and deformation. (C) 1999 Elsevier Science S.A. All rights reserved.