The assignment of appropriate reviewers to academic articles, known as the reviewer assignment problem (RAP), has become a crucial issue in academia. While there has been much research on RAP, there has not yet been a systematic literature review (SLR) examining the various approaches, techniques, algorithms and discoveries related to this topic. To conduct the SLR, we identified and evaluated relevant articles from four databases using defined inclusion and exclusion criteria. We analysed the selected articles and extracted information, and assessed their quality. Our review identified 67 articles on RAP published in conferences and journals up to mid-2022. As one of the main challenges in RAP is acquiring open data, we have studied the data sources used by researchers and found that most studies use real data from conferences, bibliographic databases and online academic search engines. RAP is divided into two main phases: (1) finding/recommending expert reviewers and (2) assigning reviewers to submitted manuscripts. In Phase 1, we have identified that decision support systems, recommendation systems, and machine learning-oriented approaches are more commonly used due to better results. In Phase 2, heuristics and metaheuristics are the approaches that present better results and are consequently more commonly used by researchers. Based on the analysed studies, we have identified potential areas for future research that could lead to improved results. Specifically, we suggest exploring the application of deep neural networks for calculating the degree of correspondence and using the Boolean satisfiability problem to optimise the attribution process.