The demand for flexible power sources with high energy density and durability has increased rapidly with the development of flexible and wearable electronic devices. Metal–air batteries are considered as the most promising candidates for these applications due to their excellent theoretical energy densities. In particular, rechargeable zinc–air and lithium–air batteries have attracted much attention because of their potential to offer high energy density while maintaining a long operational life. Although significant progress has been made in enhancing the electrochemical performance of these batteries, many technical challenges still remain to achieve the mechanical flexibility required for wearable electronic devices while maintaining high performance. This article describes the most recent advances and challenges in the development of flexible zinc–air and lithium–air batteries. We start with an overview of the latest innovations in the exploration of various battery configurations to effectively accommodate stresses and strains associated with the use of flexible electronic devices. This is followed by a detailed review of the advancements made in the design of flexible battery components: the metal electrode, the electrolyte membrane, and the air electrode. Furthermore, the effects of operating conditions on battery performance characteristics and durabilities are discussed, including the effect of the operating temperature and the contaminants commonly encountered in ambient air (e.g., carbon dioxide and moisture). Finally, challenges facing the development of a new generation of flexible metal–air batteries are highlighted, together with further research directions and perspectives.