Power supply is one of the bottlenecks to realizing untethered wearable electronics, soft robotics and the internet of things. Flexible self-charging power sources integrate energy harvesters, power management electronics and energy-storage units on the same platform; they harvest energy from the ambient environment and simultaneously store the generated electricity for consumption. Thus, they enable self-powered, sustainable and maintenance-free soft electronics. However, challenges associated with materials engineering, mechanistic understanding and device design emerge when moving from individual devices to integrated systems for practical applications. In this Review, we discuss various flexible self-charging technologies as power sources, including the combination of flexible solar cells, mechanical energy harvesters, thermoelectrics, biofuel cells and hybrid devices with flexible energy-storage components. We consider exemplary applications of power-source integration in soft electronics. Finally, we provide an overview of the emerging challenges, strategies and opportunities for research and development of flexible self-charging power sources.