In the year 1992, two publications on age-specific mortality rates revealed a cessation of demographic aging at later ages in very large cohorts of two dipteran species reared under a variety of conditions. Despite some initial concerns about possible artifacts, these findings have now been amply corroborated in the experimental literature. The eventual cessation of aging undermines the credibility of simple Gompertzian aging models based on a protracted acceleration in age-specific mortality during adulthood. The first attempt to explain the apparent cessation of aging was extreme lifelong heterogeneity among groups with respect to frailty. This lifelong heterogeneity theory assumes an underlying Gompertzian aging affecting every member of an adult cohort, with a merely apparent cessation of aging explained in terms of the increasing domination of a slowly aging group among the survivors to late ages. This theory has received several experimental refutations. The second attempt to explain the cessation of aging applied force of natural selection theory. This explanation of the cessation of aging has been corroborated in several Drosophila experiments. In particular, this theory requires that both age-specific survival and age-specific fecundity cease declining in late life, which has now been experimentally established. This theory also predicts that the timing of the cessation of aging should depend on the last age of reproduction in a population's evolutionary history, a prediction that has been corroborated. While lifelong heterogeneity should reduce average age-specific mortality in late life whenever it is pronounced, the cessation of aging in late life can be explained by plateaus in the forces of natural selection whether lifelong heterogeneity is present or not. The discovery that aging ceases is one of the most significant discoveries in recent aging research, with potentially revolutionary scientific implications.