Alkaline anion-exchange membrane fuel cells (AAEMFCs) have attracted worldwide interest due to their advantages including fast oxygen reduction kinetics, high compatibility with non-precious-metal catalyst and low cost. As one of the key components in AAEMFCs, the performance of alkaline anion exchange membranes (AAEMs) directly affects the power output and durability of the fuel cells. During fuel cell operating, AAEMs require high ionic conductivity, excellent dimensional and chemical stability to ensure high efficiency and outstanding durability. However, it is still difficult for any type of the AAEMs to meet all these requirements. This monograph summarizes recent development around the world for AAEMs, especially for the trade-off effect between ionic conductivity and stability of AAEMs as well as the proposed strategies for this issue. The charge carrier in AAEMs is OH-, and it has a lower transporting efficiency owing to its lower mobility, higher dependence on water molecular and the blocking of many hydrophobic domains in AAEMs. The improvement of ion-exchange capacity (IEC) by increasing the grafting degree (GD) of cationic functional groups can, to some extent, solve this issue. however, a high GD always bring the following negative issues: (1) Excessive swelling of AAEMs and significant reducing in the dimensional stability of membranes; (2) the increase of OH- concentration accelerates the kinetics of nucleophilic substitution and Hofmann elimination, leading to the degradation of cationic groups; (3) the enhanced polarization of the cationic groups and the hydrophilicity of the main chain enable the polymer backbone susceptible to nucleophilic attack by OH-, resulting in the degradation of the membrane, and even short-circuit of the fuel cells. In order to solve these issues, various of polymer chain architectures have been designed and regulated. To balance the ionic conductivity and the dimensional stability in AAEMs, double, triple and multi-cations are grafted on one site of polymer backbone to achieve a sufficiently high IEC at relatively low GD. Another realistic strategy is constructing 3D anion channels by the segregated hydrophilic/hydrophobic phase. The alkali stability of the cationic groups is affected by many factors including field effects, steric effects and conformation of substituent groups, and so on. The improvement of chemical stability of AAEMs has been another formidable scientific challenge. Researchers reduce the kinetics of the nucleophilic substitution and elimination reactions, and improve the basic stability of the cationic groups by modulating the structure of substituent groups such as the introduction of electron-donating groups, increased steric hindrance, and adequate hydration of OH-. Among various cationic groups, the piperidinium-based cations show high resistance against both nucleophilic substitution and elimination in alkaline conditions and at elevated temperature. Furthermore, the polymer backbones without ether band and electron-withdrawing groups have been synthesized and exabit highly resistant to alkali hydrolysis. Recently, new strategy for constructing ordered ion channels in AAEMs by novel porous materials such as metal-organic frameworks (MOF), Trogers base, and macrocyclic crown ether compounds, provide for efficient ionic transport. Additionally, highly stable metal complexes have been used as cationic group in AAEMs. These new trends will open up an exciting opportunity to design high-performance AAEMs. The appearance of highly stable AAEMs enables the AAEMFCs to be operated at 80°C, and the cell works stably in a period of study over 100 h. Although this progress is encouraging, there still remains work for improving the cell performance and stability. A 1000 h of stable operation at elevated temperatures will be the next mission for AAEMFCs. In addition, there are some fundamental issues necessary to explore, such as the transport mechanism of OH- in the membrane, the molecular interaction of polyelectrolytes and their self-assembly mechanism in solution and film formation, the mechanism of the influence of morphology on the chemical stability of AAEMs, and the factors affecting the long-term stability of AAEMFCs. These scientific issues will be the focus of future research. The development of AAEMFCs is on its way, and it calls for more efforts in fundamental study, polymer chain architectures and morphology designing, and fuel cell engineering to make it viable.