The ocean waves are an important renewable energy resource that, if extensively exploited, may contribute significantly to the electrical energy supply of countries with coasts facing the sea. A wide variety of technologies has been proposed, studied, and in some cases tested at full size in real ocean conditions. Oscillating-water-column (OWC) devices, of fixed structure or floating, are an important class of wave energy devices. A large part of wave energy converter prototypes deployed so far into the sea are of OWC type. In an OWC, there is a fixed or floating hollow structure, open to the sea below the water surface, that traps air above the inner free-surface. Wave action alternately compresses and decompresses the trapped air which is forced to flow through a turbine coupled to a generator. The paper presents a comprehensive review of OWC technologies and air turbines. This is followed by a survey of theoretical, numerical and experimental modelling techniques of OWC converters. Reactive phase control and phase control by latching are important issues that are addressed, together with turbine rotational speed control.