Record life expectancy has almost doubled from 45 years for Swedish females around 1840 to more than 87 years for Japanese females today, an increase of nearly two and a half years per decade, with no sign of a looming limit. Verified maximum human lifespans have risen more slowly and erratically, with an average increase of 1 year per decade since 1950. This modest progress plus the recent lack of substantial improvements in the mortality of centenarians suggest that life expectancy might start to increase more slowly. Evidence, however, is mixed and it is possible that most Danes born after the year 2000 will celebrate their 100th birthdays. The rise of life expectancy has been accompanied by an increase in lifespan equality—people are living longer and are dying at more similar ages. This has been achieved by reducing mortality for the third of the population with the shortest lifespans. Comparisons of humans with other species are informative. Humans are the extreme case of sharply increasing death rates in old age; for other species mortality rises more gradually, is more or less constant, or declines with age. These various findings on age-patterns of mortality for humans and other species are compelling but so counter to canonical evolutionary and gerontological theory (and common sense) that the evidence is still strongly disputed.