Discourse parsing of scientific articles is the premise and basis for standardizing the writing of scientific articles, understanding their content, and quickly locating and extracting specific information from them. This paper analyzes and summarizes related literature from three aspects: discourse structure modeling, discourse parsing and their applications by literature survey and comparative analysis. The results show that the current research focuses on the coarse-grained models of discourse structure in the domains of bio-medicine and computational linguistics. Automatic discourse parsing mainly adopts two kinds of methods: text classification and sequence labeling. Discourse structure modelling and discourse parsing has important applications in many tasks such as automatic summarization and context-based citation analysis. Future research should be extended to other domains, pay more attention to fine-grained discourse structure models based on rhetoric and argumentation structure, and apply deep learning techniques to achieve more accurate discourse parsing.