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High-quality and timely peer review for scientific works has become increasingly acute recently. Scientific reviewers peer review journal articles, conference papers, monographs, PhD-thesis, grants etc. Scientific reviewers are assigned mainly manually due to the lack of time. Having large volumes of content to review, a high-quality peer review is hard to get. In recent years there has been an increase in research on reviewer assignment automation. Also, the formal comparison of a reviewer’s research domains and a proposal’s research domains, or character-level comparison of keywords do not always provide high-quality assignments. In this paper, we perform a review on current methods of automated scientific reviewer assignment. There are 3 stages of reviewer assignment process: 1) creating reviewers’ database and structuring the information about reviewers and proposals; 2) calculating the similarity score between a proposal and a reviewer; 3) finding the appropriate assignment of proposals to reviewers, and maximizing the aggregated similarity and overall topic coverage over all assignments. Two main variations of reviewer assignment problem are considered: single and multiple reviewer assignment problem. Methods for structuring the information about proposals and reviewers based on statistical analysis of text, topic modeling and deep learning are analyzed. In the third stage, we considered possible optimal criteria for optimizing reviewers’ assignments to proposals, and also constraints, that ensure a certain level of reviewers-proposal concordance such as overall topic coverage, fair peer review, reviewers workload etc. The problem of optimal reviewer assignment is NPcomplete, therefore for solving different heuristics and meta-heuristics algorithms are used. We also present perspectives of future research on the automated reviewer assignment. [ABSTRACT FROM AUTHOR]