Solid organ transplantation has progressed rapidly over the decades from the first experimental procedures to its role in the modern era as an established treatment for end-stage organ disease. Solid organ transplantation including liver, kidney, pancreas, heart, and lung transplantation, is the definitive option for many patients, but despite the advances that have been made, there are still significant challenges in meeting the demand for viable donor grafts. Furthermore, post-operatively, the recipient faces several hurdles, including poor early outcomes like primary graft dysfunction and acute and chronic forms of graft rejection. In an effort to address these issues, innovations in organ engineering and treatment have been developed. This review covers efforts made to expand the donor pool including bioengineering techniques and the use of ex vivo graft perfusion. It also covers modifications and treatments that have been trialed, in addition to research efforts in both abdominal organs and thoracic organs. Overall, this article discusses recent innovations in machine perfusion and organ bioengineering with the aim of improving and increasing the quality of donor organs.