This systematic literature review (SLR) on LLM-based Automated Program Repair (APR) synthesizes recent research to address four key research questions. For RQ1, the authors analyzed the evolution and latest trends of LLM-based APR techniques, highlighting advances in multi-language support, retrieval-augmented debugging, and iterative refinement methods. In addressing RQ2, they identified practical deployment challenges such as computational overhead, integration with CI/CD pipelines, and the need for effective fault localization. For RQ3, the study compared proprietary and open-source LLMs, evaluating trade-offs in accuracy, efficiency, flexibility, security, and cost. Regarding RQ4, the authors examined ethical and security concerns including data privacy, model biases, and potential misuse. The review concludes that a persistent and unresolved challenge across the literature is the effective repair of multi-hunk bugs, which remains an open area for future research.