Bolted joints are ubiquitous in mechanical engineering, requiring accurate models to optimize designs. However, the exact nature of frictional contact between components is unknown and poses a significant challenge to modeling the nonlinear vibration of assemblies. This thesis applies empirical and physics-based modeling approaches to identify improvements to current models and a potential path towards predictive models of friction in bolted joints. The empirical modeling approach solves a multi-objective optimization to fit 26 friction model/interface representation combinations to experimental data and quantify the model form error. While the empirical models are not physical, the optimized results highlight the benefits of using smooth friction models and the limitations of a common physically motivated model. The physics-based model formulates the frictional force based on contact interactions of surface features and derives parameters from surface scans. While the physics-based model is not completely predictive, results show promising agreement with experiments.