Solid organ transplant constitutes the definitive treatment for end-stage organ failure. Better organ preservation methods have enabled use of marginal grafts, thereby expanding the donor pool to meet the growing demand for organs. Static cold storage as a preservation method has been superseded largely by machine perfusion in kidney transplant, with work regarding its use in other organ transplants ongoing. We hope that machine perfusion will allow better graft preservation, and pretransplant assessment, and optimization. The most extensive laboratory, preclinical, and clinical research into machine perfusion organ preservation has focused on kidneys. Successful outcomes in its use in renal transplant have sparked interest for its development and application to the liver, pancreas, heart, and lungs. This article reviews the current state of machine perfusion in abdominal and thoracic organ transplant, focusing on the recent developments in assessing graft viability.