Flexible electronic devices with mechanical properties like the soft tissues of human organs have great potential for the next generation of wearable and implantable electronic devices. Self-healing hydrogel composites typically have high tensile strength, high electrical conductivity and damage repair properties and have wide applications in flexible electronics, such as human-computer interaction, health detection and soft robots. Various self-healing hydrogel composites have been developed to produce new stretchable conductive materials with satisfactory mechanical and self-healing properties. This paper presents the fabrication of self-healing hydrogel composites and their application in flexible electronic devices. Firstly, the repair mechanism of physically cross-linked and chemically cross-linked self-healing hydrogel composites is presented. Secondly, self-healing double network hydrogels, self-healing nanocomposite hydrogels and double crosslinked self-healing hydrogel composites and their applications in flexible sensors, energy harvesting devices, energy storage devices and optical devices are presented and discussed. Finally, the challenges and prospects of self-healing hydrogel composites in flexible electronic devices in the future are presented.