High confinement (H-mode) discharges in tokamak experiments are characterized by a narrow region of steep pressure gradient called the "pedestal" that forms at the edge of the plasma, and often by an instability called an "Edge Localized Mode (ELM)" that periodically removes energy and particles from the edge of the plasma. The parameters at the top of the pedestal and the characteristics of ELMs have a strong influence on the performance of H-mode discharges. In this study, models for the pedestal are developed initially without including the effects of ELMs. The predictions from these pedestal models yield reasonable agreement with experimental data. These pedestal models are then used to provide boundary conditions in an integrated modeling code in order to simulate plasma profiles, such as temperature and density profiles, in existing H-mode experiments. The simulated profiles obtained using predictive boundary conditions and those obtained using experimental boundary conditions have similar agreement with experimental profiles. A more advanced pedestal model with a dynamic model for ELM crashes is developed using a concept of turbulence suppression at the edge of plasma. These pedestal and ELM models are coupled with a core transport model in an integrated modeling code. An advantage of this approach is that it allows for the evolution of plasma pressure and current profiles in the pedestal region, which can lead to an instability that triggers ELM crashes that limit the growth of the pedestal. Pressure-driven ballooning and current-driven peeling instabilities are considered as the possible instabilities that trigger ELM crashes. The combined core and pedestal models, with the effect of ELMs included, are used to study the dependence of triangularity and heating power on the pedestal. An MHD stability analysis is also performed to confirm the validity of these simulations. It is found that plasma edge stability improves as triangularity increases, as a result of access to the second stability region of ballooning modes. Finally, simulations yield a pedestal height with a dependence on heating power similar to that observed experimentally when the ELM crash model is extended to include ELMS triggered by current-driven peeling instabilities.