Startup from subzero temperature is one of the major challenges for proton exchange membrane fuel cell (PEMFC) to realize commercialized. Below the freezing point (0°C), water will freeze easily, which block the reactant gases into the reaction sites, thus leading to the start failure and material degradation. Therefore, for PEMFC in automotive application, successful startup from subfreezing environment is a prerequisite. Mathematical models are the effective way to study the detailed transport process and physical phenomenon, as it’s difficult and complex for experimental studies to research them. However, review papers only on cold start numerical models are not available. In this study, an extensive review on cold start models are summarized featuring the state and phase changes, heat and mass transfer. To begin with, four distinct stages for cold start process are introduced. Then, these numerical models are reviewed by dividing into four categories: zero, one, two, and three dimensional models. In particular, the one and three dimensional model are presented in detail. Moreover, the cold start strategies from start process point of view are discussed including gas purge, heat insulation, and heating. It is suggested that a proper numerical model which features internal physical phenomenon inside cell comprehensively is an effective tool to investigate cold start process. Reasonable cold start strategies should be performed to demonstrate successful startup from subzero temperature.