A detailed non-isothermal computational fluid dynamics (CFD) model for proton electrolyte membrane (PEM) fuel cells is developed in this thesis. This model consists of the equations of continuity, momentum, energy, species concentrations, and electric potentials in different regions of a PEM fuel cell. In particular, the fairly thin catalyst layers of the fuel cell are assigned a finite thickness instead of being treated as nil thickness interfaces in other PEM fuel cell models. Various source/sink terms are presented to associate the conservation equations with the electrochemical reaction kinetics. The water balance in the membrane is modeled by coupling diffusion of water, pressure variation, and the electro-osmotic drag. The membrane swelling effect is explicitly considered the newly derived model, leading to a set of novel water and proton transport equations for a membrane under the partial hydration condition. The electron transport in the catalyst layers, gas diffusion layers and bipolar plates are also described. The PEM fuel cell model developed has been implemented into a commercial CFD software package for simulating various flow and transport phenomena arising in operational PEM fuel cells, analyzing the impact of design and operating parameters on the cell performance, and optimizing the PEM fuel cell design.