Shape memory alloys (SMA) are functional materials known for their shape memory and pseudoelastic properties, which originated from a thermoelastic phase transition between two solid phases: austenite and martensite. The ranges of temperature at which austenite and martensite are stable depend primarily on the chemical composition and the thermomechanical history of the alloy. This work presents a broad overview of shape memory alloys presenting the thermoelastic phase transition at cryogenic temperatures—that is, at temperatures below the freezing point of water. Currently, this class of SMA is not very well explored due to the difficulties in conducting both structural and functional experimentations at very low temperatures. However, these materials are of great importance for extreme environments such as space. In this work, the different classes of cryogenic SMA will first be presented as a function of their phase transformation temperatures. Hints of their mechanical performance will also be reported. Cu-based systems have been identified as cryogenic SMA presenting the lowest phase transformation temperatures. The lowest measured Ms (45 K) was found for the Cu-8.8Al-13.1Mn (wt.%) alloy.