Great apes, our closest living relatives, live longer and mature later than most other mammals and modern humans are even later-maturing and potentially longer-lived. Evolutionary life-history theory seeks to explain cross-species differences in these variables and the covariation between them. That provides the foundation for a hypothesis that a novel role for grandmothers underlies the shift from an ape-like ancestral pattern to one more like our own in the first widely successful members of genus Homo. This hypothesis links four distinctive features of human life histories: 1). our potential longevity, 2). our late maturity, 3). our midlife menopause, and 4). our early weaning with next offspring produced before the previous infant can feed itself. I discuss the problem, then, using modern humans and chimpanzees to represent, respectively, genus Homo and australopithecines, I focus on two corollaries of this grandmother hypothesis: 1). that ancestral age-specific fertility declines persisted in our genus, while 2). senescence in other aspects of physiological performance slowed down. The data are scanty but they illustrate similarities in age-specific fertility decline and differences in somatic durability that are consistent with the hypothesis that increased longevity in our genus is a legacy of the "reproductive" role of ancestral grandmothers.