The rapid progress in wearable electronic devices has resulted in high demands for compatible advanced power sources with stringent requirements, such as a high energy density and operation safety, long lifespan, excellent space adaptability and mechanical robustness. Given their high theoretical energy density, intrinsic safety and adjustable form factor, rechargeable flexible zinc–air batteries (F-ZABs) are among the most promising candidates. Energy efficiency, mechanical properties and integrability with modern electronics are the three core characteristics of F-ZABs. Although efforts have been devoted to developing various cutting-edge F-ZABs, existing reviews tend to focus on electrocatalysts and battery performance and do not directly address the challenges related to other key components and architectures exclusive to F-ZABs. Herein, we have systematically summarized the recent advances in F-ZABs from a component-centric perspective. The review begins with a description of the working principle of F-ZABs, and then elucidates the recent advances in bifunctional cathode catalysts, flexible air/zinc electrodes, quasi-solid-state electrolytes, and device architecture. Aspects such as single-atomic catalysts with high catalyst-mass ratios, self-supporting electrodes with holistic structures, zinc dendrite inhibition, hydrogel electrolytes with enhanced conductivity and strength and integrable coplanar batteries are especially highlighted. Important technical hurdles and potential solutions are summarized to facilitate a broad discussion between different research communities.