Biological systems have the powerful ability to self-heal. Human skin can, for example, autonomously heal from wounds of various degrees, allowing it to restore its mechanical and electrical properties. In contrast, human-made electronic devices degrade over time due to fatigue, corrosion or damage incurred during operation, leading to device failure. Self-healing chemistry has emerged in recent years as a promising method for constructing soft electronic materials that are mechanically robust and can self-repair. Here we review the development of self-healing electronic materials and examine how such materials can be used to fabricate self-healing electronic devices. We explore the potential new functionalities of self-healing electronic systems that would not typically be possible with conventional electronic systems and discuss the current challenges in delivering self-healing soft electronics for practical applications.