The fuel cell industry is the most promising industry in terms of the advancement of clean and safe technologies for sustainable energy generation. The polymer electrolyte membrane fuel cell is divided into two parts: anion exchange membrane fuel cells (AEMFCs) and proton exchange membrane fuel cells (PEMFCs). In the case of PEMFCs, high-power density was secured and research and development for commercialization have made significant progress. However, there are technical limitations and high-cost issues for the use of precious metal catalysts including Pt, the durability of catalysts, bipolar plates, and membranes, and the use of hydrogen to ensure system stability. On the contrary, AEMFCs have been used as low-platinum or non-platinum catalysts and have a low activation energy of oxygen reduction reaction, so many studies have been conducted to find alternatives to overcome the problems of PEMFCs in the last decade. At the core of ensuring the power density of AEMFCs is the anion exchange membrane (AEM) which is less durable and less conductive than the cation exchange membrane. AEMFCs are a promising technology that can solve the high-cost problem of PEMFCs that have reached technological saturation and overcome technical limitations. This review focuses on the various aspects of AEMs for AEMFCs application.