Flexible and stretchable electronics rely on compliant conductors as essential building materials. However, these materials are susceptible to wear and tear, leading to degradation over time. In response to this concern, self-healing conductors have been developed to prolong the lifespan of functional devices. These conductors can autonomously restore their properties following damage. Conventional self-healing conductors typically comprise solid conductive fillers and healing agents dispersed within polymer matrices. However, the solid additives increase the stiffness and reduce the stretchability of the resulting composites. There is growing interest in utilizing gallium-based liquid metal alloys due to their exceptional electrical conductivity and liquid-phase deformability. These liquid metals are considered attractive candidates for developing compliant conductors capable of automatic recovery. This perspective delves into the rapidly advancing field of liquid metal-based self-healing conductors, exploring their design, fabrication, and critical applications. Furthermore, this article also addresses the current challenges and future directions in this active area of research.