Oils and mixtures of oils with hydrophobic particles are widely used in various technologies and consumer products to control foaminess and foam stability. The aim of this review is to summarize our current understanding of the mechanisms of foam destruction by such substances, which are usually called antifoams or defoamers. The experimental results show that two types of antifoam can be distinguished (called for brevity "fast" and "slow") which differ in the modes of their action. Fast antifoams are able to rupture the foam films at the early stages of film thinning. As a result, fast antifoams destroy completely the foam in less than a minute, in a typical foam-stability test. Microscopic observations have shown that the fast antifoams rupture the foam films by the so-called "bridging" mechanisms, which involve the formation of oil bridges between the two surfaces of the foam film. The stability/instability of these oil bridges is explained by using the theory of capillarity. In contrast, the oily globules of the slow antifoams are unable to enter the surfaces of the foam films and are first expelled into the Plateau borders (PBs). Only after being compressed by the narrowing walls of the PBs (due to water drainage from the foam), are the globules of the slow antifoams able to enter the solution surface and to destroy the adjacent foam films. Typically, the process of foam destruction by slow antifoams requires much longer time, minutes or tens of minutes, and a residual foam of well-defined height is observed in the foam tests. The experiments show that there is no direct relation between the magnitudes of the entry, E, spreading, S, and bridging, B, coefficients, on one side, and the antifoam efficiency, on the other side. The only requirement for having active antifoam, with respect to the bridging mechanisms, is that B should be positive. On the other hand, the barrier preventing the emergence of pre-emulsified antifoam globules on the solution surface (so-called "entry barrier") is of crucial importance for the mode of foam destruction and for the antifoam efficiency. Measurements of the entry barrier with recently developed film trapping technique (FTT) showed that antifoams possessing low entry barriers act as fast antifoams, whereas high barriers correspond to slow or inactive antifoams, although E, S, and B coefficients could be strongly positive in the latter case. A good agreement between the magnitude of the entry barrier, measured by FTT, and the height of the residual foam, in the presence of slow antifoams, was experimentally established and theoretically explained. The importance of various factors, such as the size of antifoam globules, oil spreading, kinetics of surfactant adsorption, hydrophobicity of solid particles in mixed oil-solid antifoams, and the presence of amphiphilic additives (foam boosters), is discussed from the viewpoint of the mechanisms of antifoaming. The main experimental methods, used for studying the modes of antifoam action, are briefly described.