Anion exchange polymers (AEPs) play a crucial role in green hydrogen production through anion exchange membrane water electrolysis. The chemical stability of AEPs is paramount for stable system operation in electrolysers and other electrochemical devices. Given the instability of aryl ether-containing AEPs under high pH conditions, recent research has focused on quaternized aryl ether-free variants. The primary goal of this review is to provide a greater depth of knowledge on the synthesis of aryl ether-free AEPs targeted for electrochemical devices. Synthetic pathways that yield polyaromatic AEPs include acid-catalysed polyhydroxyalkylation, metal-promoted coupling reactions, ionene synthesis via nucleophilic substitution, alkylation of polybenzimidazole, and Diels-Alder polymerization. Polyolefinic AEPs are prepared through addition polymerization, ring-opening metathesis, radiation grafting reactions, and anionic polymerization. Discussions cover structure-property-performance relationships of AEPs in fuel cells, redox flow batteries, and water and CO2 electrolysers, along with the current status of scale-up synthesis and commercialization.