In the face of a critical organ shortage in the Western world, various strategies are employed to expand the donor pool for orthotopic liver transplantation (OLT). Among them is the transplantation of organs from extended criteria donors, a valuable source of liver allografts, however, characterized by potential risks for post-OLT complications and inferior outcomes. In recent years, machine perfusion (MP) of the explanted donor liver as well as regional perfusion techniques has witnessed significant advancements. Here, we aim to discuss different modes of dynamic organ preservation in OLT. These include hypothermic and normothermic MP, hypothermic oxygenated machine perfusion (HOPE), controlled oxygenated rewarming as well as regional perfusion protocols. Over recent years, multiple feasibility trials have demonstrated the clinical prospects of MP. In the context of OLT using organs from extended criteria donors, MP has numerous advantages compared to conventional cold storage, some of which include the preservation and reconditioning of borderline transplantable organs and the viability assessment of high-risk donor allografts. This review aims to address the topic of liver allograft MP, highlighting particularly the current trends in clinical applications and future perspectives. Furthermore, different approaches of liver storage and reconditioning are reviewed in the context of ongoing research.