Aging is a dynamic and progressive process characterized by the gradual accumulation of cellular damage. The continuous functional decline in the intrinsic capacity of living organisms to precisely regulate homeostasis leads to an increased susceptibility and vulnerability to diseases. Among the factors contributing to these changes, body composition—comprised of fat mass and lean mass deposits—plays a crucial role in the trajectory of a disability. Particularly, visceral and intermuscular fat deposits increase with aging and are associated with adverse health outcomes, having been linked to the pathogenesis of sarcopenia. Adipose tissue is involved in the secretion of bioactive factors that can ultimately mediate inter-organ pathology, including skeletal muscle pathology, through the induction of a pro-inflammatory profile such as a SASP, cellular senescence, and immunosenescence, among other events. Extensive research has shown that natural compounds have the ability to modulate the mechanisms associated with cellular senescence, in addition to exhibiting anti-inflammatory, antioxidant, and immunomodulatory potential, making them interesting strategies for promoting healthy aging. In this review, we will discuss how factors such as cellular senescence and the presence of a pro-inflammatory phenotype can negatively impact body composition and lead to the development of age-related diseases, as well as how the use of polyphenols can be a functional measure for restoring balance, maintaining tissue quality and composition, and promoting health.