Simulation models are increasingly used to inform epidemiological studies and health policy, yet there is great variation in their transparency and reproducibility. This review provides an overview of applications of simulation models in health policy and epidemiology, analyzes the use of best reporting practices, and assesses the reproducibility of the models using predefined, categorical criteria. 1,613 studies were identified and analyzed. We found an exponential growth in the number of studies over the past half century, with the highest growth in dynamic modeling approaches. The largest subset of studies is focused on disease policy models (70%), within which pathological conditions, viral diseases, neoplasms, and cardiovascular diseases account for one-third of the articles. Nearly half of the studies do not report the details of their models. We also provide in depth analysis of modeling best practices, reporting quality and reproducibility for a subset of 100 articles (50 highly cited and 50 random). Only seven of 26 in-depth evaluation criteria were satisfied by more than 80% of samples. We identify areas for increased application of simulation modeling and opportunities to enhance the rigor and documentation in the conduct and reporting of simulation modeling in epidemiology and health policy.