Our ever-increasing interest in economic growth is leading the way to the decline of natural resources, the detriment of air quality, and is fostering climate change. One potential solution to reduce carbon dioxide emissions from industrial emitters is the exploitation of carbon capture and storage (CCS). Among the various CO₂ separation technologies, cryogenic carbon capture (CCC) could emerge by offering high CO₂ recovery rates and purity levels. This review covers the different CCC methods that are being developed, their benefits, and the current challenges deterring their commercialisation. It also offers an appraisal for selected feasible small- and large-scale CCC applications, including blue hydrogen production and direct air capture. This work considers their technological readiness for CCC deployment and acknowledges competing technologies and ends by providing some insights into future directions related to the R&D for CCC systems.