Self-healing, a counterintuitive but significant effect in structured light, that granting a light field the ability to reconstruct itself after a partial obstruction placed in its propagation path. Here, we will give a comprehensive review of the history and development of self-healing effects, especially highlighting its importance in vector vortex beams carrying spin and orbital angular momenta. Moreover, an unified zoology of self-healing, structured light is proposed to unveil a deeper understanding of its physical mechanism and provide a bird's eye view on diverse forms of self-healing effects of different kinds of complex structured light. Finally, we outline the open challenges we are facing, potential opportunities and future trends for both fundamental physics and applications.