The post-breakdown conduction of thin-oxide metal-oxide-semiconductor structures with different gate electrodes and substrates is studied. Due to the extreme localization of the breakdown, many breakdown events can be produced in one capacitor during a constant voltage stress. In some cases, these events have been found to be reversible and this suggests that the breakdown is a reversible phenomenon (i.e., that the breakdown is a reversible switching between two conduction states of different conductivities). This reversibility is further supported by the observation of bistable conduction in the post-breakdown I-V characteristic when the breakdown current is externally limited. The experimental results are interpreted assuming that the breakdown is a three-stage process (degradation-breakdown-thermal effects), and a simple phenomenological model is presented. The role of the gate electrode (chromium, aluminum, or polycrystalline-silicon) and that of the substrate doping are analyzed within this framework. The presented results show that the analysis of the post-breakdown properties is a powerful technique to investigate the physics of the breakdown.