Abstract Although liver transplantation is a true success story, many patients still die awaiting an organ. The increasing need for liver grafts therefore remains an unsolved challenge to the transplant community. To address this, transplant donor criteria have been expanded and, for example, more liver grafts with significant steatosis or from donors with circulatory death are being used. These marginal grafts, however, carry an increased risk of graft‐associated complications, such as primary nonfunction, delayed graft function, or late biliary injuries. Therefore, reliable assessment of graft viability before use is essential for further success. To achieve this, machine liver perfusion, a procedure developed more than 50 years ago but almost forgotten at the end of the last century, is again of great interest. We describe in this review the clinical most applied machine perfusion techniques, their mechanistic background, and a novel concept of combining immediate organ assessment during hypothermic oxygenated perfusion, followed by an extended phase of normothermic machine perfusion, with simultaneous ex situ treatment of the perfused liver. Such a new approach may allow the pool of usable livers to dramatically increase and improve outcomes for recipients.