The term shape memory alloys (SMAs) is applied to that group of metallic materials that demonstrate the ability to return to some previously defined shape or size when subjected to the appropriate thermal procedure. SMAs are extremely corrosion resistant with excellent biocompatibility which can be fabricated into very small size with properties of elasticity and force delivery that allow uses in several industrial applications, including biomedical applications. This Article provides information on the history of SMAs, the general characteristics of SMAs, and their crystallography, including the phase transformations and phases occurring during thermal treatment. It also describes the thermomechanical behavior of SMAs, and explains the different characterization methods, including the differential scanning calorimeter (DSC) technique. The Article describes the types of SMA alloys, namely, nickel-titanium alloys and copper-base shape memory alloys with their properties.