In the past, a diagnosis of organ failure would essentially be a death sentence for patients. With improved techniques for organ procurement and surgical procedures, transplantations to treat organ failure have become standard medical practice. However, while the demand for organs has skyrocketed, the donor pool has not kept pace leading to long recipient waiting lists. Organ preservation provides a means to increase the number of available transplantable organs. However, there are significant drawbacks associated with cold storage, the current gold standard. To address the short-comings due to diffusional limitations, engineers have developed cold perfusion systems. More recently, there has been a significant trend towards the development of near-normothermic systems to enhance the functional preservation of solid organs including livers, lungs, hearts, kidneys, and vascularized composite allotransplants. Here we review recent advances in the development of perfusion systems for the preservation of solid organs. We provide a brief history of organ transplantation, the limitations of existing systems, and describe research being done to develop commercially available perfusion systems to enhance organ preservation.