The research efforts directed at advancing water electrolysis technology continue to intensify together with the increasing interest in hydrogen as an alternative source of energy to fossil fuels. Among the various water electrolysis systems reported to date, systems employing a solid polymer electrolyte membrane are known to display both improved safety and efficiency as a result of enhanced separation of products: hydrogen and oxygen. Conducting water electrolysis in an alkaline medium lowers the system cost by allowing non-platinum group metals to be used as catalysts for the complex multi-electron transfer reactions involved in water electrolysis, namely the hydrogen and oxygen evolution reactions (HER and OER, respectively). We briefly review the anion exchange membranes (AEMs) and electrocatalysts developed and applied thus far in alkaline AEM water electrolysis (AEMWE) devices. Testing the developed components in AEMWE cells is a key step in maximizing the device performance since cell performance depends strongly on the structure of the electrodes containing the HER and OER catalysts and the polymer membrane under specific cell operating conditions. In this review, we discuss the properties of reported AEMs that have been used to fabricate membrane-electrode assemblies for AEMWE cells, including membranes based on polysulfone, poly(2,6-dimethyl-p-phylene) oxide, polybenzimidazole, and inorganic composite materials. The activities and stabilities of tertiary metal oxides, metal carbon composites, and ultra-low Pt-loading electrodes toward OER and HER in AEMWE cells are also described.