The question of negative differential capacitance (C) at electrified interfaces is critically reviewed. The importance of the thermodynamic constraints and the physical differences between systems under charge and potential control is emphasized. For a system under potential control,Ccan never be negative, while no such general constraint is mandated for systems under charge control. However, the appearance of a negativeCdomain in isolated systems can be limited by a phase transition to a non-uniform state. The occurrence of such transitions depends on the ‘stiffness’ of the interface. Theoretical calculations that predictC< 0 are analysed. We investigate a series of electromechanical analogues of the existing models of double layer, illustrating the appearance ofC< 0 in ‘rigid’ systems under equilibrium conditions, and the transition to the non-uniform state in systems with moderate ‘surface tension’, narrowing theC< 0 domain. The effect of intrinsic non-homogeneity is also addressed. The appearance of domains whereCis negative under charge control implies the occurrence of surface phase transitions under potential control. The characteristics of phase transitions in isolated and open systems, and the relationship between them, are considered. Some biophysical implications are discussed.