This book examines the characteristics of Proton Exchange Membrane (PEM) Fuel Cells with a focus on deriving realistic finite element models. The book also explains in detail how to set up measuring systems, data analysis, and PEM Fuel Cells' static and dynamic characteristics. Covered in detail are design and operation principles such as polarization phenomenon, thermodynamic analysis, and overall voltage; failure modes and mechanisms such as permanent faults, membrane degradation, and water management; and modelling and numerical simulation including semi-empirical, one-dimensional, two-dimensional, and three-dimensional models. It is appropriate for graduate students, researchers, and engineers who work with the design and reliability of hydrogen fuel cells, in particular proton exchange membrane fuel cells.