The remarkable growth in life expectancy during the twentieth century inspired predictions of a future in which all people, not just a fortunate few, will live long lives ending at or near the maximum human life span. We show that increased longevity has been accompanied by less variation in ages at death, but survivors to the oldest ages have grown increasingly heterogeneous in their mortality risks. These trends are consistent across countries, and apply even to populations with record-low variability in the length of life. We argue that as a result of continuing improvements in survival, delayed mortality selection has shifted health disparities from early to later life, where they manifest in the growing inequalities in late-life mortality.