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Startup from subzero temperature is one of the major challenges for polymer electrolyte membrane fuel cell (PEMFC) to realize commercialization. Below the freezing point (0°C), water will freeze easily, which blocks the reactant gases into the reaction sites, thus leading to the start failure and material degradation. Therefore, for PEMFC in vehicle application, finding suitable ways to reach successful startup from subfreezing environment is a prerequisite. As it’s difficult and complex for experimental studies to measure the internal quantities, mathematical models are the effective ways to study the detailed transport process and physical phenomenon, which make it possible to achieve detailed prediction of the inner life of the cell. However, review papers only on cold start numerical models are not available. In this study, an extensive review on cold start models is summarized featuring the states and phase changes of water, heat and mass transfer.