The dramatic expansion of modern linguistic research and enhanced accuracy of linguistic analysis have become a reality due to the ability of artificial neural networks not only to learn and adapt, but also carry out automate linguistic analysis, select, modify and compare texts of various types and genres. The purpose of this article and the journal issue as a whole is to present modern areas of research in computational linguistics and linguistic complexology, as well as to define a solid rationale for the new interdisciplinary field, i.e. discourse complexology. The review of trends in computational linguistics focuses on the following aspects of research: applied problems and methods, computational linguistic resources, contribution of theoretical linguistics to computational linguistics, and the use of deep learning neural networks. The special issue also addresses the problem of objective and relative text complexity and its assessment. We focus on the two main approaches to linguistic complexity assessment: “parametric approach” and machine learning. The findings of the studies published in this special issue indicate a major contribution of computational linguistics to discourse complexology, including new algorithms developed to solve discourse complexology problems. The issue outlines the research areas of linguistic complexology and provides a framework to guide its further development including a design of a complexity matrix for texts of various types and genres, refining the list of complexity predictors, validating new complexity criteria, and expanding databases for natural language.