Anion exchange membrane (AEM) water electrolysis is a hydrogen production method that is achieved with an AEM, using electricity. One of the major advantages of AEM water electrolysis is the replacement of conventional noble metal electrocatalysts with low cost transition metal catalysts. AEM electrolysis is still a developing technology; therefore, with a view to using it to eventually achieve commercially viable hydrogen production, AEM electrolysis requires further investigation and improvements, specifically regarding its power efficiency, membrane stability, robustness, ease of handling, and cost reduction. This review addresses state of the art technology of AEM electrolysis for hydrogen production. It also provides a summary of important research that has been carried out on membranes, electrocatalysts, and ionomers used in AEM electrolyzers, and the performance of such electrolyzers. The aim of this review is to identify gaps in AEM water electrolysis research and to make recommendations for future directions in AEM water electrolysis research.