Given the increasing graft shortage, the transplant community is forced to use so called marginal liver grafts with a higher susceptibility to ischemia-reperfusion injury. This exposes the recipient to a higher risk of graft failure and post-transplant complications. While static cold storage remains the gold standard in low-risk transplant scenarios, dynamic preservation strategies may allow to improve outcomes after transplantation of marginal liver grafts. Two dynamic preservation strategies, end-ischemic hypothermic oxygenated perfusion (HOPE) and continuous normothermic machine perfusion (cNMP), have been evaluated in randomized clinical trials. The results show improved preservation of liver grafts after cNMP and reduction of post-transplant biliary complications after HOPE. In comparison to cNMP, HOPE has the advantage of requiring less logistics and expertise with the possibility to return to default static cold storage. Both strategies allow to assess graft viability prior to transplantation and may thus contribute to optimizing graft selection and reducing discard rates. The use of dynamic preservation is rapidly increasing in France and results from a national randomized trial on the use of HOPE in marginal grafts will soon be available. Future applications should focus on controlled donation after circulatory death liver grafts, split grafts and graft treatment during perfusion. The final aim of dynamic liver graft preservation is to improve post-transplant outcomes, increase the number of transplanted grafts and allow expansion of transplant indications.