Organ transplantation has developed over the past 50 years to reach the sophisticated and integrated clinical service of today through several advances in science. One of the most important of these has been the ability to apply organ preservation protocols to deliver donor organs of high quality, via a network of organ exchange to match the most suitable recipient patient to the best available organ, capable of rapid resumption of life-sustaining function in the recipient patient. This has only been possible by amassing a good understanding of the potential effects of hypoxic injury on donated organs, and how to prevent these by applying organ preservation. This review sets out the history of organ preservation, how applications of hypothermia have become central to the process, and what the current status is for the range of solid organs commonly transplanted. The science of organ preservation is constantly being updated with new knowledge and ideas, and the review also discusses what innovations are coming close to clinical reality to meet the growing demands for high quality organs in transplantation over the next few years.