Background/Objectives: Population aging is accompanied by a rapidly increasing burden of neurodegenerative disorders, particularly Alzheimer’s and Parkinson’s diseases. Within the geroscience framework, targeting fundamental mechanisms of aging may delay the onset or progression of multiple age-related conditions. Dietary factors, especially plant-derived polyphenols, have gained increasing attention due to their potential to modulate molecular pathways involved in brain aging. This narrative review aims to integrate current evidence on dietary polyphenols and their role in modulating the molecular mechanisms underlying brain aging and neurodegeneration. Methods: This narrative review synthesizes findings from molecular, experimental, epidemiological, and clinical studies to provide an integrated assessment of the effects of dietary polyphenols on key cellular pathways involved in brain aging. Results: Polyphenols are widely present in plant-based foods, and polyphenol-rich dietary patterns—particularly the Mediterranean and MIND diets—have been consistently associated in observational studies with a reduced risk of cognitive decline. Mechanistic evidence, derived predominantly from in vitro and animal studies with limited validation in humans, suggests that polyphenols may influence key hallmarks of aging, including oxidative stress, chronic inflammation, mitochondrial dysfunction, cellular senescence, and impaired proteostasis. These effects are mediated through pathways such as Nrf2, NF-κB, AMPK, mTOR, and SIRT1, as well as via gut–brain axis interactions. However, clinical evidence remains heterogeneous. Conclusions: Dietary polyphenols represent a biologically plausible and promising, yet not fully validated, nutritional strategy for promoting healthy brain aging. Their translation into clinical practice is limited by low bioavailability, substantial interindividual variability, and the lack of large-scale, long-term randomized controlled trials.