Smart dielectric materials with bioinspired and autonomous functions are expected to be designed and fabricated for next-generation electrical insulation. Similar to organisms, such dielectrics with self-adaptive, self-reporting, and self-healing capabilities can be employed to avoid, diagnose, and repair electrical damage to prevent catastrophic failure and even a blackout. Compared with traditional dielectrics, the utilization of smart materials not only increases the stability and durability of power apparatus but also reduces the costs of production and manufacturing. In this review, researches on self-adaptive, self-reporting, and self-healing dielectrics in the field of electrical insulation, and illuminating studies on smart polymers with autonomous functions in other fields are both introduced. The principles, methods, mechanisms, applications, and challenges of these materials are also briefly presented.