Mammals vary widely in average adult life span and age at maturity, but the ratio between the two is quite robust with 95% confidence intervals for one sample between 1.3 and 1.54. Primates generally have longer lifespans and later maturity than nonprimate mammals of similar body size, but the ratio between the two does not differ from mammals in general. Those who survive to adulthood can expect to be alive when some of their grandchildren are born. Age and experience affect performance across adulthood and observations in some species show that older females take greater risks to protect younger kin. High-ranking females maintain social positions advantageous to their kin simply by surviving. In human hunter-gatherers, average adult lifespans are longer and age at maturity later than the other living hominids, but the ratio between them is similar to that of other primates. However, since all the living great apes have last births in their forties, women, but not other female great apes, usually outlive their fertility. Unlike other primates, humans are sterile for most of their grandmotherhood. Also unlike other primates, human grandmothers share food with their younger kin. Without newborns of their own, they are often more economically productive than are women in their childbearing years. This contribution that grandmothers make to the welfare of their descendants may help explain the evolution of human longevity and the evolution of our distinctively human pattern of cooperative breeding.