As an alternative to conventional gas-compression cyclic cooling, caloric effects through solid-solid phase transformations/transitions offer an innovative platform as an environmentally friendly cooling technique. Among the various types of caloric effects, the elastocaloric effect has garnered significant attention. This technique exploits the large latent heat associated with ferroelastic transformations, typically superelasticity, which refers to the stress-induced reversible thermoelastic martensitic transformations that exhibit a large recoverable strain. In this review, the fundamental mechanism of elastocaloric cooling is reviewed with addressing the fundamental phenomenology of superelasticity in shape-memory alloys. To evaluate the elastocaloric cooling performance associated with superelasticity, a phase diagram in the stress-induced martensitic transforming systems is informative. This review guides the way to quantitatively evaluate the two factors that primarily determine the performance as an elastocaloric cooling material: the entropy change and dissipation heat. This demonstration is done for the prototypical shape-memory alloys of Ti-Ni and Cu-Al-Mn alloys. More specifically, the low-temperature operation of superelasticity and the potential of associated elastocaloric cooling effect are discussed in terms of the balance between the entropy change and dissipation heat. Finally, the cooling performance of various kinds of caloric materials is compared and the challenges, and prospects of shapememory materials as solid-state cooling materials are addressed.