The quality of peer review, and consequently the published research, depends to a large extent on the ability to recruit adequate reviewers for submitted papers. However, finding such reviewers is an increasingly difficult task. To alleviate this challenge, numerous solutions have been suggested for automated association of papers with "well matching" reviewers -the task often referred to as reviewer assignment problem (RAP). Yet, to our knowledge, a recent systematic synthesis of the RAP-related literature is missing. To fill this gap and support further RAP-related research, we present a scoping review on computational approaches to RAP. Following the latest methodological guidance for scoping reviews, we have collected and synthesised the literature on RAP published over the last five years (Jan 2016 -Sept 2021). Specifically, the review is focused on the following aspects of RAP research: i) the overall approach to RAP; ii) the criteria used for reviewer selection; iii) the modelling of candidate reviewers and submissions; iv) the computational methods for matching reviewers and submissions; and v) the evaluation methods used for assessing the performance of the proposed solutions. The paper summarises and discusses the findings for each of the aforementioned aspects of RAP research and suggests future research directions.