Polymer-electrolyte fuel cells are a promising energy-conversion technology. Over the last several decades significant progress has been made in increasing their performance and durability, of which continuum-level modeling of the transport processes has played an integral part. In this review, we examine the state-of-the-art modeling approaches, with a goal of elucidating the knowledge gaps and needs going forward in the field. In particular, the focus is on multiphase flow, especially in terms of understanding interactions at interfaces, and catalyst layers with a focus on the impacts of ionomer thin-films and multiscale phenomena. Overall, we highlight where there is consensus in terms of modeling approaches as well as opportunities for further improvement and clarification, including identification of several critical areas for future research.