Metal film capacitors are ubiquitous components in modern electronics, playing an important role in energy storage, filtering, and voltage regulation. However, their performance and reliability can be reduced by partial electrical breakdowns caused by defects in the dielectric material. An attempt to partially mitigate this problem are self-healing capacitors, which have the ability to recover after an electrical breakdown. The self-healing phenomenon significantly increases the service life of the device. This review presents a comprehensive analysis of the currently known self-healing mechanisms in metal film capacitors. The role of the self-healing phenomenon in increasing the number of capacitor working cycles is discussed. The molecular processes underlying the significantly different self-healing potential of dielectric polymers are verified. The review is addressed to specialists in electrical engineering.