Heart transplantation is advocated in selected patients with advanced heart failure in the absence of contraindications. Principal challenges in heart transplantation centre around an insufficient and underutilized donor organ pool, the need to individualize titration of immunosuppressive therapy, and to minimize late complications such as cardiac allograft vasculopathy, malignancy, and renal dysfunction. Advances have served to increase the organ donor pool by advocating the use of donors with underlying hepatitis C virus infection and by expanding the donor source to use hearts donated after circulatory death. New techniques to preserve the donor heart over prolonged ischaemic times, and enabling longer transport times in a safe manner, have been introduced. Mechanical circulatory support as a bridge to transplantation has allowed patients with advanced heart failure to avoid progressive deterioration in hepato-renal function while awaiting an optimal donor organ match. The management of the heart transplantation recipient remains a challenge despite advances in immunosuppression, which provide early gains in rejection avoidance but are associated with infections and late-outcome challenges. In this article, we review contemporary advances and challenges in this field to focus on donor recovery strategies, left ventricular assist devices, and immunosuppressive monitoring therapies with the potential to enhance outcomes. We also describe opportunities for future discovery to include a renewed focus on long-term survival, which continues to be an area that is under-studied and poorly characterized, non-human sources of organs for transplantation including xenotransplantation as well as chimeric transplantation, and technology competitive to human heart transplantation, such as tissue engineering.