Ischemia-reperfusion injury (IRI) constitutes a significant source of morbidity and mortality after orthotopic liver transplantation (OLT). The allograft is metabolically impaired during warm and cold ischemia and is further damaged by a paradox reperfusion injury after revascularization and reoxygenation. Short-term and long-term complications including post-reperfusion syndrome, delayed graft function, and immune activation have been associated with IRI. Due to the current critical organ shortage, extended criteria grafts are increasingly considered for transplantation, however, with an elevated risk to develop significant features of IRI. In recent years, ex vivo machine perfusion (MP) of the donor liver has witnessed significant advancements. Here, we describe the concept of hypothermic (oxygenated) machine perfusion (HMP/HOPE) approaches and highlight which allografts may benefit from this technology. This review also summarizes clinical applications and the main aspects of ongoing randomized controlled trials on hypothermic perfusion. The mechanistic aspects of IRI and hypothermic MP—which include tissue energy replenishment, optimization of mitochondrial function, and the reduction of oxidative and inflammatory damage following reperfusion—will be comprehensively discussed within the context of current preclinical and clinical evidence. Finally, we highlight novel trends and future perspectives in the field of hypothermic MP in the context of recent findings of basic and translational research.