The concept of surface tension is usually introduced as a force per unit length originated from the “stress tensor” at the liquid surface (and vaguely extended to solids). This mechanical model of the surface tension, a paradigm for many workers in the field, is wrong. The inferences from the model, however, are correct in the more common uses. Some contradictions may appear but not sufficient to abandon such a simple and intuitive concept. The origin of the surface tension, of a liquid or solid surface, is in the molecular interactions, when some other phase is put in contact with such a surface. Recent developments using the surface tension components allow to predict interfacial surface tensions and to measure surface tension of solids. Although the power of this approach is evident, its use is only incipient because some results, particularly the presence of negative interfacial tensions, are difficult to interpret using the erroneous vision of surface tension as a consequence of a “stress tensor” at the liquid (or solid) surface. We present here some properties of liquids useful to fundament the concept of surface tension and briefly refer to Laplace's equation, Young's equation and capillarity, attempting to correct some misinterpretations.