In recent years, nutraceuticals have gained great popularity, owing to their physiological and potential health effects, such as anti-inflammatory, anti-cancer, antioxidant, and prebiotic effects, and their regulation of lipid metabolism. Since the Mediterranean diet is a nutritionally recommended dietary pattern including high-level consumption of nutraceuticals, this review aimed to summarize the main results obtained by our in vitro and in vivo studies on the effects of the major constituents of the Mediterranean diet (i.e., extra virgin olive oil compounds, polyunsaturated fatty acids, and fruit components). Based on experimental studies, the therapeutic purpose of nutraceuticals depends on their bioavailability, solubility, toxicity, and delivery system. This review provides more in-depth knowledge on the effects linked to nutraceuticals administration on human health, focusing the gastrointestinal tract and suggesting specific dietary components for personalized adjuvant therapies.