This article describes the classification of fuel cells depending on the operating temperature and type of electrolytes used. This classification includes alkaline fuel cells, phosphoric acid fuel cells, polymer electrolyte membrane fuel cells (PEMFCs), molten carbonate fuel cells (MCFCs), and solid oxide fuel cells (SOFCs). The article explains the corrosion processes in fuel cells due to solid-gas interactions, solid-liquid interactions, and solid-solid interactions. It discusses the long-term performance stability and long-term degradation processes of PEMFCs, MCFCs, and SOFCs. The article reviews the development of chemically and structurally compatible component materials in PEMFCs, MCFCs, and SOFCs.