The Mediterranean Diet (MD), UNESCO Intangible Cultural Heritage of Humanity, has become a scientific topic of high interest due to its health benefits. The aim of this review is to pick up selected studies that report nutrigenomic or nutrigenetic data and recapitulate some of the biochemical/genomic/genetic aspects involved in the positive health effects of the MD. These include (i) the antioxidative potential of its constituents with protective effects against several diseases; (ii) the epigenetic and epigenomic effects exerted by food components, such as Indacaxanthin, Sulforaphane, and 3-Hydroxytyrosol among others, and their involvement in the modulation of miRNA expression; (iii) the existence of predisposing or protective human genotypes due to allelic diversities and the impact of the MD on disease risk. A part of the review is dedicated to the nutrigenomic effects of the main cooking methods used in the MD and also to a comparative analysis of the nutrigenomic properties of the MD and other diet regimens and non-MD-related aliments. Taking all the data into account, the traditional MD emerges as a diet with a high antioxidant and nutrigenomic modulation power, which is an example of the “Environment-Livings-Environment” relationship and an excellent patchwork of interconnected biological actions working toward human health.