Examples of crystallization of glasses and of the condensation of excitons to form an electron-hole liquid in germanium are used to study the kinetics of nucleation of a new phase. There are considerable advantages in tackling such model systems rather than other systems undergoing a first-order phase transition. Attention is drawn to two different nucleation regimes: transient and quasisteady-state. Special consideration is given to nucleation in an open system from which nuclei of the new phase may be removed rapidly as a result of diffusion or drift to absorbing walls. In such cases very strong supersaturation may be reached and the threshold of the appearance of a new phase may be independent of temperature.