Publisher Summary This chapter provides an introduction to fuel cells and discusses their modeling with a focus on polymer electrolyte membrane (PEM). Fuel cell modeling is relevant in addressing global power needs. It consists of a negatively charged electrode (anode), a positively charged electrode (cathode), and an electrolyte membrane. Hydrogen is oxidized on the anode and oxygen is reduced on the cathode. Protons are transported from the anode to the cathode through the electrolyte membrane, and the electrons are carried to the cathode over the external circuit. The interest in fuel cells has increased due to the fact that the use of fossil fuels for power has resulted in many negative consequences. Fuel cells are now closer to commercialization than ever, and they have the ability to fulfill all global power needs while meeting the efficacy and environmental expectations. PEM fuel cells are the most popular type of fuel cells that use hydrogen as the fuel. They also have many other fuel options, which range from ethanol to biomass-derived materials. These fuels can either be directly fed into the fuel cell, or sent to a reformer to extract pure hydrogen, which is then directly fed to the fuel cell.