Modeling and simulation play a very crucial role in the development of the polymer electrolyte membrane (PEM) fuel cells. This review presents a detailed literature overview of the approaches used for PEM fuel cell modeling and problems related to it. The review starts with a brief overview of the hydrogen energy storage system and working of PEM fuel cells. After that, the models range from a simplified one-dimensional model to full three-dimensional models that are used to simulate the PEM fuel cells and are elaborated. The issues associated with the experimental validation of the model, especially in the concentration loss regions of the polarization curve, are also discussed. In addition to that, the physical interpretation of the ANSYS PEM fuel cell module governing equations are explained in terms of the practical processes taking place within PEM fuel cells. Finally, the gaps identified in the current knowledge of the PEM fuel cell simulation modeling are highlighted.