Discourse structure analysis aims to understand the overall structure of an article and the semantic relationships between its various parts. As a research hotspot of natural language processing, it has developed rapidly in recent years. This study first summarizes the mainstream discourse structure analysis theories in English and Chinese and then introduces the research on the popular English and Chinese discourse corpora as well as their calculation models. On this basis, this study surveys the current work context of discourse structure analysis in Chinese and English and constructs its research framework. Moreover, the current research trends and focuses are summarized, and the application of discourse structure in downstream tasks is introduced briefly. Finally, this study points out the issues and challenges in the current Chinese discourse structure analysis to provide guidance and help for future research.