The gut and the brain communicate via the nervous system, hormones, microbiota-mediated substances, and the immune system. These intricate interactions have led to the term “gut-brain axis”. Unlike the brain—which is somewhat protected—the gut is exposed to a variety of factors throughout life and, consequently, might be either more vulnerable or better adapted to respond to these challenges. Alterations in gut function are common in the elder population and associated with many human pathologies, including neurodegenerative diseases. Different studies suggest that changes in the nervous system of the gut, the enteric nervous system (ENS), during aging may result in gastrointestinal dysfunction and initiate human pathologies of the brain via its interconnection with the gut. This review aims at summarizing the contribution of normal cellular aging to the age-associated physiological changes of the ENS. Morphological alterations and degeneration of the aging ENS are observed in different animal models and humans, albeit with considerable variability. The aging phenotypes and pathophysiological mechanisms of the aging ENS have highlighted the involvement of enteric neurons in age-related diseases of the central nervous system such as Alzheimer’s or Parkinson’s disease. To further elucidate such mechanisms, the ENS constitutes a promising source of material for diagnosis and therapeutic predictions, as it is more accessible than the brain.