Elastocaloric materials exhibit extraordinary cooling potential, but the repetition of cyclic mechanical loadings during long-term operation of cooling systems requires the refrigerant material to have long fatigue life. This article reviews the fundamental cause of fatigue from aspects of initiation and propagation of fatigue cracks in shape-memory alloys (SMAs) that are used as elastocaloric materials, and highlights recent advances in using compression to overcome fatigue by curtailing the generation of surfaces associated with crack propagation. Compression is identified as a key means to extend fatigue lifetime in engineering design of elastocaloric cooling drive mechanisms. We summarize the state-of-the-art performance of different SMAs as elastocaloric materials and discuss the influence of low cyclic strains and high resistance to transformation. We present integration of compression-based material assemblies into a cooling system prototype and optimization of the system efficiency using work recovery and related measures.