Flexible electronics has gained great interest in emerging wearable or rolling-up gadgets, such as foldable displays, electronic papers, and other personal multimedia devices. Subsequently, there is a need to develop energy storage devices that are pliable, inexpensive, and lightweight. Metal–air batteries have been identified as one of alternative energy storages for cost effective and high energy density applications. They offer cheaper production cost and higher energy density than most of the currently available battery technologies. Thus, they are promising candidates for flexible energy storage devices. Flexible metal–air batteries have to maintain their performances during various mechanical deformations. To date, efforts have been focused on fabricating flexible components for metal–air batteries. This review presents a brief introduction to the field, followed by progress on development of flexible electrolytes, electrodes, and prototype devices. Challenges and outlook towards the practical use of metal–air batteries are given in the last part.