A process for making olive oil having a high polyphenol content and, in particular a high hydroxytyrosol content, comprises the conventional steps of transforming (II) olives (1) into an oily must (5); of resolving (V) the later into an oily juice (7), from which a base olive oil (8) is obtained, and into an aqueous juice (6) containing most of the polyphenols; and of separating (VII) the vegetation water (9) from the aqueous juice (6). Moreover, according to the invention, steps are provided of removing water (XV) from the vegetation water (9), preferably by evaporation, so as to obtain a polyphenol-enriched concentrate (11); and of mixing (XIX) the concentrate (11) with the base olive oil (8), so as to transfer said polyphenols from the former to the latter and to obtain a final polyphenol-enriched oil (12), along with an exhausted concentrate (11'). The step of removing water causes a polyphenol concentration increase, to enhance their interphase transfer, and, at the same time, it causes a viscosity and density increase, which makes the water phase, during the contact with the oil, less prone to form emulsions than the methods of prior art. The high polyphenol concentration remarkably improves the organoleptic quality of the oil and makes the latter more stable, besides producing well-known advantageous effects for the consumer's health. According to further aspects of the invention, an apparatus is provided for making such oils, as well as a concentrate for use in olive oils and also in any other vegetable or animal food oil, in cosmetics, bio-repellent products and the like.