This article is devoted to the consideration of discourse studies development as well as that of discourse analysis. This method makes it possible to take into account not only the linguistic (verbal) aspect, but also the supra-linguistic (extra-verbal) one, as it also focuses on the situational peculiarities of the text or statements, their pragmatic and functional features, the cultural and historical context, and many other factors. Nowadays discourse analysis is widely used for interdisciplinary research, which determines the relevance of studying the prospects for its further use. This work provides a historical overview of discourse studies formation and development. Various approaches to the key concept interpretation from this area, which is discourse, are analysed. The process of discourse analysis formation as one of the most important parts of the conceptual and categorical apparatus of discourse studies as well as various approaches to its implementation are considered. Some new ways of using discourse analysis to conduct research on various institutional types of communication are proposed, which is demonstrated by the example of implementing this method in the study of sports rhetoric.