Donor heart preservation is still a critical determinant of outcomes after heart transplantation, particularly as transplant programs increasingly rely on extended-criteria and donation-after-circulatory-death donors. This narrative review provides an overview of the evolution of donor heart preservation, from conventional static cold storage to contemporary technologies designed to reduce ischemia–reperfusion injury, improve graft assessment, and expand organ utilization. We discuss the physiological rationale and clinical evidence supporting commonly used cardioplegic solutions, including University of Wisconsin, Celsior, and histidine–tryptophan–ketoglutarate solutions. We then examine advanced preservation strategies, including controlled hypothermic preservation systems and ex vivo normothermic machine perfusion, which allow improved temperature control, continuous monitoring, functional assessment, and, in the case of machine perfusion, potential metabolic optimization of the graft during transport. Current evidence suggests that these technologies could extend acceptable preservation times, facilitate long-distance procurement, and support the use of marginal and DCD grafts. However, their widespread adoption is limited by logistical complexity, costs, and the need for further independent studies evaluating long-term clinical outcomes. Modern preservation platforms can represent a major paradigm shift in heart transplantation, with the potential to improve graft availability and post-transplant outcomes.