Abstract: This review is devoted to the physics of current-carrying superconductors and normal metals having two or more stable states sustained by Joule self-heating. The creation, propagation, and localization of electrothermal domains and switching waves leading to the transition from one stable state to another in uniform and nonuniform samples are treated in detail. The connection between thermal bistability and hysteresis, dropping and stepped current-voltage characteristics, self-induced oscillations of current and voltage, selfreplication of electrothermal domains, and the formation of periodic and stochastic resistive structures are considered.