The cryogenic industry has experienced remarkable expansion in recent years. Cryogenic technologies are commonly used for industrial processes, such as air separation and natural gas liquefaction. Another recently proposed and tested cryogenic application is Liquid Air Energy Storage (LAES). This technology allows for large-scale long-duration storage of renewable energy in the power grid. One major advantage over alternative storage techniques is the possibility of efficient integration with important industrial processes, e.g., refrigerated warehousing of food and pharmaceuticals. Heat exchangers are among the most important components determining the energy efficiency of cryogenic systems. They also constitute the necessary interface between a LAES system and the industrial process utilizing the available cooling effect. The present review aims to familiarise energy professionals and stakeholders with the latest achievements, innovations, and trends in the field of cryogenic heat exchangers, with particular emphasis on their applications to LAES systems employing renewable energy resources. Important innovations in coil-wound and plate-fin heat exchanger design and simulation methods are reviewed among others, while special attention is given to regenerators as a prospective component of cryogenic energy storage systems. This review also reveals that the geographical spread of research and development activities has recently expanded from well-established centers of excellence to rather active emerging establishments around the globe.