Virgin olive oil (VOO) is the pillar fat of Mediterranean diet. It is made from olive fruits and obtained by squeezing olives without any solvent extraction. Respect to the seed oils, an unique polar polyphenol-rich fraction gives VOO a bitter and pungent taste. The recent substantiation by European Food Safety Authority (EFSA) of a health claim for VOO polyphenols may represent an efficient stimulus to get the maximum health benefit from one of the most valuable traditional product of Mediterranean countries educating consumers to the relationship between the VOO bitterness and its health effect. Agronomical practices and new processing technology to avoid phenolic oxidation and hydrolysis and to enhance the aromatic components of the VOO have been developed and they can be used to modulate taste and flavor to diversify the products on the market. VOOs having high concentration of phenol compounds are bitter and pungent therefore many people do not consume them, thus loosing the health benefits related to their intake. In this paper, the chemist's and nutritionist's point of view has been considered to address possible strategies to overcome the existing gap between the quality perceived by consumer and that established by expert tasters. Educational campaigns emphasizing the bitter-health link for olive oils should be developed.