People have always sought eternal life and everlasting youth. Recent technological breakthroughs and our growing understanding of ageing have given strength to the idea that a cure for human ageing can eventually be developed. In this talk, I will discuss the prospect of eradicating human ageing, its potential social consequences, and ethical implications. I will argue that developing the means to abolish ageing is an ethical endeavour because the goal of biomedical research is to allow people to be as healthy as possible for as long as possible. Nonetheless, radical increases in human lifespan raise major social and ethical questions, which will be discussed.