Multi-physics and multi-phase flow models for a proton exchange membrane fuel cell (PEMFC) are developed in this book. The models represent different mathematical approaches for model development based on PEMFCs, which fully couple majority of physical and electrochemical processes occurred during PEMFC operation, and the models are developed from simple to complex, from ideal assumption to practical conditions. Comprehensive water transport mechanism associated with water phase transfer between various phases, as well as gas-liquid water two-phase flow process is taken into account. The models developed in this book provide insights of better understanding and outstanding issues of a PEMFC. Moreover, it is capable of revealing mass transport resistance, optimising electrode composition and improving cell performance at various operation conditions and loads. Most importantly, this book can be used as a handbook for PEMFC model development, especially for young researchers at their early stage of research.