Along with the rapid development of flexible and wearable electronic devices, there have been a strong demand for flexible power sources, which has in turn triggered considerable efforts on the research and development of flexible batteries. An ideal flexible battery would have not only just high electrochemical performance but also excellent mechanical deformabilities. Therefore, battery constituent components, chemistry systems, device configurations, and practical applications are all pivotal aspects that should be thoroughly considered. Herein, we systematically and comprehensively review the fundamentals and recent progresses of flexible batteries in terms of these important aspects. Specifically, we first discuss the requirements for constituent components, including the current collector, electrolyte, and separator, in flexible batteries. We then elucidate battery chemistry systems that have been studied for various flexible batteries, including lithium-ion batteries, non-lithium-ion batteries, and high-energy metal batteries. This is followed by discussions on the device configurations for flexible batteries, including one-dimensional fiber-shaped, two-dimensional film-shaped, and three-dimensional structural batteries. Finally, we summarize recent efforts in exploring practical applications for flexible batteries. Current challenges and future opportunities for the research and development of flexible batteries are also discussed.