It has been suggested that highly social mammals, such as naked mole rats and humans, are long-lived due to neoteny (the prolongation of youth). In both species, aging cannot operate as a mechanism facilitating natural selection because the pressure of this selection is strongly reduced due to 1) a specific social structure where only the “queen” and her “husband(s)” are involved in reproduction (naked mole rats) or 2) substituting fast technological progress for slow biological evolution (humans). Lists of numerous traits of youth that do not disappear with age in naked mole rats and humans are presented and discussed. A high resistance of naked mole rats to cancer, diabetes, cardiovascular and brain diseases, and many infections explains why their mortality rate is very low and almost age-independent and why their lifespan is more than 30 years, versus 3 years in mice. In young humans, curves of mortality versus age start at extremely low values. However, in the elderly, human mortality strongly increases. High mortality rates in other primates are observed at much younger ages than in humans. The inhibition of the aging process in humans by specific drugs seems to be a promising approach to prolong our healthspan. This might be a way to retard aging, which is already partially accomplished via the natural physiological phenomenon neoteny.