The transition from a carbon-centered economy to an era of renewable energy has led to global attention on hydrogen energy, ultimately leading to the development of fuel cells using hydrogen as a fuel. In response to global demand, overall fuel cell technology has grown remarkably over the past few years; yet, commercialization remains sluggish owing to cost. As the cathode of a proton exchange membrane fuel cell (PEMFC), which is the most commercialized fuel cell, is markedly dependent on platinum (Pt), anion exchange membrane fuel cells (AEMFCs), which can utilize non-precious materials as cathode catalysts, have emerged as a promising alternative. Earth-abundant metals are used as cathode catalysts, and metal-free materials are used to achieve comparable performance to Pt. Compared to the single-cell performance of Pt catalysts, a gap still exists; however, the applicability of non-noble metals has been extensively evaluated. If catalyst development is accompanied by efficient electrode structure design, a significant part of the cost problem can be overcome. AEMFCs have advantages in the ORR of cathodes compared to PEMFCs; however, the HOR kinetics are quite sluggish. Therefore, the design of HOR catalysts requires another approach, not only to enhance their intrinsic activity, but also consider the poisoning induced by the use of ionomers besides PEMFCs. Therefore, a strategy based on the HOR pathway is required to lower the barrier of the rate-determining step. In this review, catalysts for AEMFCs were introduced based on their classification, and information on recent trends and issues related to catalysts was presented.