This article presents a review of constitutive theories, mechanics, and structural applications of shape memory alloys. Although these materials possess a number of unique features, this review is concerned with the shape memory effect and superelasticity, since they are most often discussed in the context of possible applications. The article begins with a discussion of these effects and a reference to a number of studies elucidating the properties of shape memory alloys. In the next section, a number of constitutive theories are listed and some recent theories are discussed in detail. The work related to numerous technological problems that arise in the process of manufacturing shape memory alloy structures is considered. Structural problems of shape memory structures, such as buckling, vibration, acoustic control, etc are discussed. The work related to development and design of shape memory sensors and actuators is also reviewed. Finally, some applications of shape memory alloy actuators, particularly those in the aerospace and medical fields, are considered. This review article contains 195 references.