The Mediterranean diet is worldwide recognized as a good prototype of nutrition due to the conspicuous intake of olive oil, nuts, red wine, legumes, fruit, and vegetables, all fundamental elements rich in antioxidant substances and polyphenols. Polyphenols are a wide range of phytochemicals and/or synthetic chemical compounds with proven beneficial properties for human health. In the present review, we critically summarize the wellcharacterized antioxidant and anti-inflammatory properties of polyphenols contained in the olives and extra virgin olive oil and of resveratrol, a non-flavonoid phenolic compound. We discuss the potential use of these polyphenols as pharmaceutical formulations for the treatment of human diseases. We also show the emerging importance of their consumption in the prevention and management of crucial neurodegenerative conditions (alcohol-related brain disorders and aging) and in neuromuscular disorders (Spinal Muscular Atrophy and Amyotrophic Lateral Sclerosis and Duchenne Muscular Dystrophy), where oxidative stress plays a predominant role.