Mg-air batteries, with their intrinsic advantages such as high theoretical volumetric energy density, low cost, and environmental friendliness, have attracted tremendous attention for electrical energy storage systems. However, they are still in an early stage of development and suffer from large voltage polarization and poor cycling performance. At present, Mg-air batteries with high rechargeability remain difficult to achieve, mainly because the discharge products [Mg(OH)2, MgO and MgO2] are thermodynamically and kinetically difficult to decompose at moderate voltage ranges. Therefore, it is crucial to optimize the reaction paths and kinetics from the electrodes to the batteries via the combination of materials design and first-principles calculations. In this review, remarkable progress is highlighted regarding the currently used materials for Mg-air batteries, including anodes, electrolytes, and cathodes. In addition, the corresponding reaction mechanisms are comprehensively surveyed. Finally, future perspectives for rechargeable Mg-air batteries with decreased voltage polarization and improved cycling performance are also described for further practical applications.