This review explores the integration of artificial intelligence (AI) and machine learning (ML) into kidney transplantation (KT), set against the backdrop of a significant donor organ shortage and the evolution of ‘Next-Generation Healthcare’. Its purpose is to evaluate how AI and ML can enhance the transplantation process, from donor selection to postoperative patient care. Our methodology involved a comprehensive review of current research, focusing on the application of AI and ML in various stages of KT. This included an analysis of donor–recipient matching, predictive modeling, and the improvement in postoperative care. The results indicated that AI and ML significantly improve the efficiency and success rates of KT. They aid in better donor–recipient matching, reduce organ rejection, and enhance postoperative monitoring and patient care. Predictive modeling, based on extensive data analysis, has been particularly effective in identifying suitable organ matches and anticipating postoperative complications. In conclusion, this review discusses the transformative impact of AI and ML in KT, offering more precise, personalized, and effective healthcare solutions. Their integration into this field addresses critical issues like organ shortages and post-transplant complications. However, the successful application of these technologies requires careful consideration of their ethical, privacy, and training aspects in healthcare settings.