The urgent need to expand the donor pool in order to attend to the growing demand for liver transplantation has obliged physicians to consider the use of suboptimal liver grafts and also to redefine the preservation strategies. This review examines the different methods of liver graft preservation, focusing on the latest advances in both static cold storage and machine perfusion (MP). The new strategies for static cold storage are mainly designed to increase the fatty liver graft preservation via the supplementation of commercial organ preservation solutions with additives. In this paper we stress the importance of carrying out effective graft washout after static cold preservation, and present a detailed discussion of the future perspectives for dynamic graft preservation using MP at different temperatures (hypothermia at 4 °C, normothermia at 37 °C and subnormothermia at 20 °C-25 °C). Finally, we highlight some emerging applications of regenerative medicine in liver graft preservation. In conclusion, this review discusses the "state of the art" and future perspectives in static and dynamic liver graft preservation in order to improve graft viability.