Aging is characterized by a progressive decline of physiological integrity leading to the loss of tissue function and vulnerability to disease, but its causes remain poorly understood. Skeletal muscle has an outstanding regenerative capacity that relies on its resident stem cells (satellite cells). This capacity declines with aging, and recent discoveries have redefined our view of why this occurs. Here, we discuss how an interconnection of extrinsic changes in the systemic and local environment and cell-intrinsic mechanisms might provoke failure of normal muscle stem cell functions with aging. We focus particularly on the emergent biology of rejuvenation of old satellite cells, including cells of geriatric age, by restoring traits of youthfulness, with the final goal of improving human health during aging.