This thesis deals with mathematical modeling of PEM fuel cells. The resulting process models can be used to make decisions such as operating conditions, sensitivity analysis and to explore regimes of process operation that are not reachable. This thesis consists of two parts. The first part is artificial neural network (ANN) modeling of PEM fuel cells. The second part is the two-dimensional modeling of hydrogen PEM fuel cells, with a focus on the water management issues in the cell. ^ In our simulations, ANN models have shown to be accurate for predicting the cell performance of fuel cell systems. The effect of Pt loading on the performance of the PEM fuel cell has been specifically studied. The results show that the ANN model is capable of simulating this effect for which there are currently no valid fundamental models available from the literature. Hybrid models that consist of a physical component and an ANN component were proposed to more accurately predict the performance of a PEM fuel cell, in the case when fundamental models of limited accuracy are available. Multiplicative and additive hybrid model have been developed and compared. The results from the hybrid models show comparable performance compared to the ANN model. Additionally, the hybrid models show great performance gains over the physical model alone. Using the ANN process models, optimization models were constructed to determine the optimal operating conditions of the PEM fuel cells. ^ To describe the water transport process in the fuel cell, a two-dimensional model for the water transport in the membrane was developed and incorporated into the full fuel cell model. This model has been used to investigate the water transport mechanisms in the membrane and the water balance in the cell. The effects of relative humidity, cathode pressure and current density on the water transport mechanisms were discussed. Case studies at various operating conditions demonstrate that this model is capable of predicting critical water management issues, such as membrane dehydration and flooding. Parametric studies with this model were conducted to examine the sensitivity of the model to major operating and design parameters.