The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. Full three-dimensional, multiphase, non-isothermal computational fluid dynamics models of planar air-breathing and airflow-channel PEM fuel cell have been developed. These comprehensive models account for the major transport phenomena in both these types: convective and diffusive heat and mass transfer, electrode kinetics, transport and phase-change mechanism of water, and potential fields. The models are shown to understand the many interacting, complex electrochemical, and transport phenomena that cannot be studied experimentally. Fully three-dimensional results of the species profiles, temperature distribution, potential distribution, and local current density distribution are presented and analyzed with a focus on the physical insight and fundamental understanding for the air-breathing and airflow-channel PEM fuel cells.