Adult muscle stem cells, originally called satellite cells, are essential for muscle repair and regeneration throughout life. Besides a gradual loss of mass and function, muscle aging is characterized by a decline in the repair capacity, which blunts muscle recovery after injury in elderly individuals. A major effort has been dedicated in recent years to deciphering the causes of satellite cell dysfunction in aging animals, with the ultimate goal of rejuvenating old satellite cells and improving muscle function in elderly people. This review focuses on the recently identified network of cell-intrinsic and -extrinsic factors and processes contributing to the decline of satellite cells in old animals. Some studies suggest that aging-related satellite-cell decay is mostly caused by age-associated extrinsic environmental changes that could be reversed by a “youthful environment”. Others propose a central role for cell-intrinsic mechanisms, some of which are not reversed by environmental changes. We believe that these proposals, far from being antagonistic, are complementary and that both extrinsic and intrinsic factors contribute to muscle stem cell dysfunction during aging-related regenerative decline. The low regenerative potential of old satellite cells may reflect the accumulation of deleterious changes during the life of the cell; some of these changes may be inherent (intrinsic) while others result from the systemic and local environment (extrinsic). The present challenge is to rejuvenate aged satellite cells that have undergone reversible changes to provide a possible approach to improving muscle repair in the elderly.