Elastocaloric cooling is as a solid-state cooling technology undergoing early stage research and development.  This study presents a general introduction of core concepts common to all caloric cooling technologies and a review of the recent progress made in the elastocaloric Cooling field with respect to materials, mathematical modelling at the system and material levels, and system integration. Multiple compositions were recently studied. Some by adding alloying elements to traditional systems to tune the transformation temperature and increase fatigue life. Other are multiferroic alloys, which are materials that can respond simultaneously to additional stimuli (electric or magnetic field) besides strain to leverage multiple caloric effects at once. Influence of additional variables like texture, strain rate, martensitic transformation paths and hysteresis in material’s performance have also been further studied. Fundamental thermodynamic principles were applied to further understanding elastocaloric effect, and through mathematical description of the heat transfer process coupled with phase transformation new approaches to materials and characterization. System integration with heat recovery and regeneration strategies were also reviewed.