The opioid overdose crisis is driven by an intersecting set of social, structural, and economic forces. Simulation models are a tool to help us understand and address thiscomplex, dynamic, and nonlinear social phenomenon. We conducted a systematic review of the literature on simulation models of opioid use and overdose up to September 2019. We extracted modeling types, target populations, interventions, and findings; created a database of model parameters used for model calibration; and evaluated study transparency and reproducibility. Of the 1,398 articles screened, we identified 88 eligible articles. The most frequent types of models were compartmental (36%), Markov (20%), system dynamics (16%), and agent-based models (16%). Intervention cost-effectiveness was evaluated in 40% of the studies, and 39% focused on services for people with opioid use disorder (OUD). In 61% of the eligible articles, authors discussed calibrating their models to empirical data, and in 31%, validation approaches used in the modeling process were discussed. From the 63 studies that provided model parameters, we extracted the data sources on opioid use, OUD, OUD treatment, cessation or relapse, emergency medical services, and death parameters. From this database, potential model inputs can be identified and models can be compared with prior work. Simulation models should be used to tackle key methodological challenges, including the potential for bias in the choice of parameter inputs, investment in model calibration and validation, and transparency in the assumptions and mechanics of simulation models to facilitate reproducibility.