Fuel cells have attracted widespread attention owing to the merits of high efficiency, high safety and wide application, etc. Therefore, fuel cells can meet the increasing requirement for clean energy in human society. Among them, anion exchange membrane fuel cells have shown broad application prospects due to the environmental friendliness, the use of non?precious metal catalysts, high safety and stability, etc. As the core component of anion exchange membrane fuel cells, anion exchange membranes can isolate the anode from the cathode and conduct hydroxide ions. Thus, the property of anion exchange membranes plays a crucial role in the performance of anion exchange membrane fuel cells. In the development process of anion exchange membranes, the low conductivity and poor hydroxide ions conductivity stability have become the key technical challenge. The development of flexible anion exchange membranes can play a positive role in promoting the further commercialization of anion exchange membrane fuel cells. Based on this, this article reviews the recent research progress on flexible anion exchange membranes from three aspects: polymer molecular chain design, structural optimization design, and new material synthesis and the composites.