Shape memory alloys (SMAs) are a promising class of advanced materials with interesting properties, which make them suitable for a variety of engineering applications. The uses of SMAs in engineering applications have extended year by year. SMAs are being used in a number of industrial applications such as aerospace, automotive, biomaterial, chemical-sensor, construction, electronics, metal forming, storage and retrieval of information, optics etc. This paper highlights some of these engineering applications of SMAs. This also includes the recent research on the possible use of SMAs in smart structures. The important properties of SMAs that provide the impetus for using these materials in innovative applications are (1) shape memory effect, (2) pseudoelasticity and (3) high damping capacity. For a better appreciation, some of the basic principles and properties related to the unique behavior of this class of materials are also discussed.