Software often contains defects, and automated repair techniques offer a promising way to address these issues. This paper examines the current state of research in learning-based Automated Program Repair (APR). It reviews existing learning-based APR approaches and systematically categorizes them into five major types: supervised learning, unsupervised learning, transfer learning, ensemble learning, and language model learning. Finally, the paper discusses the challenges faced in this field, providing valuable insights for future research.