With the rapid development of wearable and intelligent flexible electronic devices (FEDs), the demand for flexible energy storage/conversion devices (ESCDs) has also increased. Rechargeable flexible metal-air batteries (MABs) are expected to be one of the most ideal ESCDs due to their high theoretical energy density, cost advantage, and strong deformation adaptability. With the improvement of the device design, material assemblies, and manufacturing technology, the research on the electrochemical performance of flexible MABs has made significant progress. However, achieving the high mechanical flexibility, high safety, and wearable comfortability required by FEDs while maintaining the high performance of flexible MABs are still a daunting challenge. In this review, flexible Zn-air and Li-air batteries are mainly exemplified to describe the most recent progress and challenges of flexible MABs. We start with an overview of the structure and configuration of the flexible MABs and discuss their impact on battery performance and function. Then it focuses on the research progress of flexible metal anodes, gel polymer electrolytes, and air cathodes. Finally, the main challenges and future research perspectives involving flexible MABs for FEDs are proposed.