Large language models (LLMs) have significantly impacted human society, influencing various domains. Among them, academia is not simply a domain affected by LLMs, but it is also the pivotal force in the development of LLMs. In academic publication, this phenomenon is represented during the incorporation of LLMs into the peer review mechanism for reviewing manuscripts. LLMs hold transformative potential for the full-scale implementation of automated scholarly paper review (ASPR), but they also pose new issues and challenges that need to be addressed. In this survey paper, we aim to provide a holistic view of ASPR in the era of LLMs. We begin with a survey to find out which LLMs are used to conduct ASPR. Then, we review what ASPR-related technological bottlenecks have been solved with the incorporation of LLM technology. After that, we move on to explore new methods, new datasets, new source code, and new online systems that come with LLMs for ASPR. Furthermore, we summarize the performance and issues of LLMs in ASPR, and investigate the attitudes and reactions of publishers and academia to ASPR. Lastly, we discuss the challenges and future directions associated with the development of LLMs for ASPR. This survey serves as an inspirational reference for the researchers and can promote the progress of ASPR for its actual implementation.