Many computational fluid dynamics polymer-electrolyte-membrane fuel cell models have been presented over the last few decades. A detailed literature overview of models, ranging from onedimensional, single-component to complete three-dimensional, large-scale setups, is presented with an emphasis on heat and mass transfer. Modeling strategies and commonly used assumptions are discussed. Solver implementations, popular numerical algorithms, and computational techniques are summarized. Additionally, model accuracy and convergence problems are highlighted while solving for these highly coupled, nonlinear systems of partial differential equations. Finally, an overview of commonly used simulation software for fuel cell modeling is given. A simple case study is presented throughout this review to support and to illustrate several discussed aspects. The paper finishes with a survey of outstanding issues and recent modeling trends.