Automated program repair (APR) aims to automatically fix bugs of software to improve software stability. Recently, Neural Program Repair (NPR) techniques based on Code Pre-trained Models (CodePTMs) have gained significant attention in the APR field. However, no study to date has yet comprehensively explored the effectiveness and possible limitations of CodePTMs for NPR. To fill this gap, this survey provides a systematic review of the current research on CodePTMs-based NPR techniques, highlighting key challenges and proposing future research directions. Overall, our survey aims to provide researchers with a detailed understanding of current approaches and to promote the further development of CodePTMs in the NPR.