A coherent set of epidemiological data shows that the Mediterranean diet has beneficial effects capable of preventing a variety of age-related diseases in which low-grade, chronic inflammation/inflammaging plays a major role, but the underpinning mechanism(s) is/are still unclear. It is suggested here that the Mediterranean diet can be conceptualized as a form of chronic hormetic stress, similar to what has been proposed regarding calorie restriction, the most thoroughly studied nutritional intervention. Data on the presence in key Mediterranean foods of a variety of compounds capable of exerting hormetic effects are summarized, and the mechanistic role of the nuclear factor erythroid 2 pathway is highlighted. Within this conceptual framework, particular attention has been devoted to the neurohormetic and neuroprotective properties of the Mediterranean diet, as well as to its ability to maintain an optimal balance between pro- and anti-inflammaging. Finally, the European Commission-funded project NU-AGE is discussed because it addresses a number of variables not commonly taken into consideration, such as age, sex, and ethnicity/genetics, that can modulate the hormetic effect of the Mediterranean diet.