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• A comprehensive introduction of rhetorical structure theory (RST). • A snapshot and some statistical data of RST-DT. • An elaboration of the classical and latest RST parsing methods. • Applications of RST, especially in expert and intelligent systems. • Comparisons with other discourse structure theories. Rhetorical structure theory (RST) is a significant theory about discourse organization. With an increasing number of research interests focus on RST, many novel parsing approaches have been proposed and motivated many brand new applications, such as chatbots and other expert and intelligent systems. However, the work on RST dates back many years and there remains a lack of comprehensive literature reviews. The aim of this study is therefore to provide a comprehensive overview of RST, parsing methods and applications. In this paper, we first give a detailed introduction to RST. Then the commonly used discourse treebank: RST-DT is elaborated. We propose a new taxonomy to divide the RST parsing methods into different categories. With a focus on the classical and latest methods that have recently been developed, we review the pros and cons of these approaches, along with the performance analysis of them. We then summarize the applications of RST across various domains. Moreover, we present a comparative study of RST with other discourse structure theories. Finally, we discuss some implications of our findings and outline future research directions in this challenging and fast-growing field. [ABSTRACT FROM AUTHOR]