Our societies are witnessing a steady increase in longevity. This demographic evolution is accompanied by some convergence across countries, but at the same time substantial longevity inequalities persist within nations across income classes. This Element aims to survey some crucial implications of changing longevity on the design of optimal public policy. For that purpose, it first focuses on some difficulties raised by risky and varying lifetime for the representation of individual and social preferences. Then, it explore some central implications of changing longevity for optimal policy making, regarding prevention against premature death, pension policies, education, health care and long-term care. The author distinguishes between the case when longevity is partially the responsibility of individuals and the case when longevity is plainly exogenous.