The emergence of soft machines and electronics creates new opportunities to engineer robotic systems that are mechanically compliant, deformable, and safe for physical interaction with the human body. Progress, however, depends on new classes of soft multifunctional materials that can operate outside of a hard exterior and withstand the same real-world conditions that human skin and other soft biological materials are typically subjected to. As with their natural counterparts, these materials must be capable of self-repair and healing when damaged to maintain the longevity of the host system and prevent sudden or permanent failure. Here, we provide a perspective on current trends and future opportunities in self-healing soft systems that enhance the durability, mechanical robustness, and longevity of soft-matter machines and electronics.