We present an overview of the mathematical issues that arise in the modeling of polymer electrolyte membrane fuel cells. These issues range from nanoscale modeling of network structures arising in pore formation within the polymer and the formation of nanostructured agglomerates within the catalyst layer, to macroscale models of multiphase flow and water management, degradation of catalyst layers and membrane, and development of stack level codes. The dominant themes are the development and analysis of multiscale models and their reduction to simplified forms that are implementable in stack-level computations.