The freshwater cnidarian polyp named Hydra, which can be mass-cultured in the laboratory, is characterized by a highly dynamic homeostasis with a continuous self-renewal of its three adult stem cell populations, the epithelial stem cells from the epidermis, the epithelial stem cells from the gastrodermis, and the multipotent interstitial stem cells, which provide cells of the nervous system, gland cells and germ cells. Two unusual features characterize these stem cells that cannot replace each other, they all avoid G1 to pause in G2, and the two epithelial populations are concomitantly multifunctional and stem cells. H. vulgaris that does not show any signs of aging over the years, resists to weeks of starvation and adapts to the loss of neurogenesis, providing a unique model system to study the resistance to aging. By contrast some strains of a distinct species named H. oligactis undergo a rapid aging process when undergoing gametogenesis or when placed in stress conditions. The aging phenotype is characterized by the rapid loss of somatic interstitial stem cells and the progressive reduction in epithelial stem cell self-renewal, the loss of regeneration, the disorganization of the neuro-muscular system, the loss of the feeding behavior, and the death of all animals within about three months. We review here the possible mechanisms that help H. vulgaris to sustain stem cell self-renewal and thus bypass aging processes. For this, FoxO seems to act as a pleiotropic actor, regulating stem cell proliferation, stress response and apoptosis. In H. oligactis, the regulation of the autophagy flux differs between aging-sensitive and aging-resistant animals, pointing to a key role for proteostasis in the maintenance a large pool of active and plastic epithelial stem cells.