The main aim of the paper is to catalog ways of modeling bolted joints and introducing bolt preload using the finite element method. The paper presents models of bolted joints published in the current decade (i.e. after 1 January 2021 and up to 10 May 2023) in journals of the world's largest scientific publishers, such as: Elsevier, Springer, and MDPI, among others. Reporting of the systematic review was carried out based on PRISMA guidelines. The databases were searched with the EBSCO multi-search engine for the following keywords: bolted joint model, bolted connection model, preload, and finite element method. Additionally, the search results were narrowed down to peer-reviewed papers from the discipline of engineering and written in English. This yielded 2,712 records for further analysis. After removing duplicates from this group, screening was carried out, based on which 1,476 records were excluded from the study. For the remaining group of reports, an eligibility assessment was performed, after which a further 210 reports were excluded from the study. Finally, 86 papers were included in the review. As a result of their examination, six groups of simplified fastener models currently used in the modeling of bolted joints at the assembly stage were described.