One promising way to store and distribute large amounts of renewable energy is water electrolysis, coupled with transport of hydrogen in the gas grid and storage in tanks and caverns. The intermittent availability of renewal energy makes it difficult to integrate it with established alkaline water electrolysis technology. Proton exchange membrane (PEM) water electrolysis is promising, but limited by the necessity to use expensive platinum and iridium catalysts. The expected solution is anion exchange membrane (AEM) water electrolysis, which combines the use of cheap and abundant catalyst materials with the advantages of PEM water electrolysis, namely a low foot print, large operational capacity, and fast response to changing operating conditions. The key component for AEM water electrolysis is a cheap, stable, gas tight and highly hydroxide conductive polymeric AEM. Here we present target values and technical requirements for AEMs, discuss the chemical structures involved and the related degradation pathways, and give an overview over the most prominent and promising commercial AEMs (Fumatech Fumasep® FAA3, Tokuyama A201, Ionomr Aemion™, Dioxide materials Sustainion®, and membranes commercialized by Orion Polymer), and review their properties and performances of water electrolyzers using these membranes.