Heart transplantation (HTx) remains the last therapeutic resort for patients with advanced heart failure. The present work is a clinically focused review discussing current issues in heart transplantation. Several factors have been associated with the outcome of HTx, such as ABO and HLA compatibility, graft size, ischemic time, age, infections, and the cause of death, as well as imaging and laboratory tests. In 2018, UNOS changed the organ allocation policy for HTx. The aim of this change was to prioritize patients with a more severe clinical condition resulting in a reduction in mortality of people on the waiting list. Advanced heart failure and resistant angina are among the main indications of HTx, whereas active infection, peripheral vascular disease, malignancies, and increased body mass index (BMI) are important contraindications. The main complications of HTx include graft rejection, graft angiopathy, primary graft failure, infection, neoplasms, and retransplantation. Recent advances in the field of HTx include the first two porcine-to-human xenotransplantations, the inclusion of hepatitis C donors, donation after circulatory death, novel monitoring for acute cellular rejection and antibody-mediated rejection, and advances in donor heart preservation and transportation. Lastly, novel immunosuppression therapies such as daratumumab, belatacept, IL 6 directed therapy, and IgG endopeptidase have shown promising results.