Human life span is quite unusual in that it includes a prolonged post-reproductive period in females and the existence of menopause. This is observed in some other species in captivity, provided with the benefits of life-long veterinary care, but in the wild very few species indeed share this characteristic with us. Of these, killer whales are the nearest to us in the evolutionary tree of life. None of our closer relatives, such as other primates, experience menopause. They are in addition short-lived in comparison to our length of life. Chimpanzees and gorillas top out at 50-60 years of age in captivity, and a decade or more less in the wild.
Much of current thinking on the topic of unusual human longevity, at least when compared with our primate cousins, centers on our intelligence and capacity for culture as the originating difference. This allows older people to contribute materially to the success of their descendants, and this applies selection pressure to extended life: those with the capacity to live longer prosper, and some new balance of biological mechanisms is reached under the hood as a result. This view of the recent evolutionary past is known as the grandmother hypothesis, and ties together the existence of menopause, exceptional longevity, and the well-known disparity between male and female life spans. You can look back in the Fight Aging! archives for a pointer to a good open access paper on this topic.
You might consider the paper linked below as a reading companion to that earlier publication. The nature of longevity and its origins in our evolutionary past are very interesting topics. It doesn't have any great and immediate relevance to efforts to repair the causes of aging and thus indefinitely extend human life spans, of course. How and why we ended up in this situation isn't terribly important in comparison to understanding our present biology well enough to maintain it properly over time. I think you'll agree it is a good read nonetheless:
Why ageing occurs has been a central question in ecology and evolution for much of the past century. There is general agreement that the evolution of senescence is unavoidably linked to the fact that under natural conditions organisms die from extrinsic hazards. Since there are always fewer older individuals in a population than younger ones, the strength of selection on alleles with age-specific fitness effects is expected to weaken with increasing age and alleles that confer advantages early in life, by increasing early-life fecundity, can spread to fixation even if they have deleterious effects later. The declining strength of selection with age sets the stage for the evolution of physiological mechanisms leading to both reproductive and somatic senescence.
Somatic and reproductive senescence are inherently linked: there is no benefit to an organism in maintaining a viable germline if somatic senescence has progressed to the point that prevents successful reproduction. Most vertebrate species typically show a gradual decline in reproduction with age. However, in some circumstances reproductive senescence is accelerated relative to somatic senescence leading to a post-reproductive life span (PRLS). Why females of some species cease ovulation before the end of their natural lifespan is a longstanding evolutionary puzzle. Theoretical research over the past 50 years provides a coherent framework to understand senescence in general, but decoupling somatic and reproductive senescence has proved a major theoretical challenge.
PRLSs in modern humans are often dismissed as an artefact: medicine and the protected environments of the contemporary world allow women to live beyond the supply of primary oocytes. There is, however, considerable evidence that humans living with high rates of mortality and without access to modern medicine exhibit PRLSs. Others have argued that post-reproductive longevity is an epiphenomenon of antagonistic pleiotropy favouring early-life fertility at the expense of fertility later in life or that PRLSs have evolved as an insurance against the risk of dying by chance before the cessation of reproductive activity. There is, however, mounting evidence that in humans, resident killer whales, and social aphids post-reproductive females increase the survival or reproductive success of their kin. However, evidence that post-reproductive females increase the survival of kin is not sufficient to demonstrate that PRLSs are adaptive. It is also necessary to show that PRLSs results in a net inclusive fitness benefit. The difficulty in demonstrating inclusive fitness benefits of PRLSs via mother and grandmother effects has prompted a search for new adaptive explanations. The question of why prolonged life after the cessation of fertility has evolved in some species has not been fully answered.
Given that the capacity for post-fertility survival appears to be widespread, why are prolonged PRLSs restricted to just three vertebrate species? We suggest that understanding how females compete for reproduction and help their kin, and how the magnitude of these costs and benefits change across the lifespan, is fundamental to understanding variation across species in the evolution of PRLSs. We should expect females to forgo late-life reproduction only where doing so boosts the fitness of their kin and where helping is more effective if females are no longer reproducing themselves.