Peer review is a process used in the selection of manuscripts for journal publication and proposals for research grant funding. Though widely used, peer review is not without flaws and critics. Performing large-scale experiments to evaluate and test correctives and alternatives is difficult, if not impossible. Thus, many researchers have turned to simulation studies to overcome these difficulties. In the last 10 years this field of research has grown significantly but with only limited attempts to integrate disparate models or build on previous work. Thus, the resulting body of literature consists of a large variety of models, hinging on incompatible assumptions, which have not been compared, and whose predictions have rarely been empirically tested. This scoping review is an attempt to understand the current state of simulation studies of peer review. Based on 46 articles identified through literature searching, we develop a proposed taxonomy of model features that include model type (e.g. formal models vs. ABMs or other) and the type of modeled peer review system (e.g. peer review in grants vs. in journals or other). We classify the models by their features (including some core assumptions) to help distinguish between the modeling approaches. Finally, we summarize the models' findings around six general themes: decision-making, matching submissions/reviewers, editorial strategies; reviewer behaviors, comparisons of alternative peer review systems, and the identification and addressing of biases. We conclude with some open challenges and promising avenues for future modeling work.