Life expectancy at birth has more than doubled in Europe since the early 19th century. This demographic trend constitutes a major victory against scarcity, but raises also deep challenges to the Welfare State, concerning the sustainability and the equity of the social protection system. This paper surveys recent developments in the economic analysis of longevity, both at the positive and the normative levels. Taking mortality risks into account is shown to affect the study of the life cycle model significantly, in particular concerning the strength of life horizon effects. It raises also, at the level of normative foundations for policy-making, a dilemma between ex ante and ex post valuations. Finally, we explore the design of policy reforms under varying longevity, in fields including preventive and curative policies, education, pension, and wealth taxation.