With an expectation of life at birth of 27 years in the middle of the 18th century, 21% of males reached their 60th birthday with a remaining expectation of life of 12 years. Under the conditions of mortality of 1950, in France, 70 percent could celebrate their 60th birthday, and they had still 15 years (only) to live on the average. This last figure started increasing after 1950: the expectancy of life at age 60 is now over 20 years, and it will exceed 25 years around 2050 (for women, the mean will be 31 years). Longevity is an individual capacity. It is now increasing fast, and becomes more and more responsible for the ageing of the population (the rise in the proportion of older persons in the population). We now try to forecast the number of centenarians, and even of super-centenarians (aged 110 years and more), and speculate about the maximum life span. We are in fact entering an entirely new era, when three, four, even five generations can survive simultaneously. Are we prepared to it? The French Ministers for Research and for Social affairs set up a Committee of 15 members (chaired by Henri Leridon) to prepare a National Meeting of Researchers on Ageing, in order to review the situation of research in France on this issue and to make proposals for organising and orienting new studies. The life span of human species, as well as the one of individuals, is undoubtedly depending upon genetic factors. But interactions with environmental factors and with behaviour also play a major role. To be able to disentangle these complex associations, it will be necessary to combine the work of biologists, clinicians and social sciences specialists. The main conclusions of the June 2001 meeting are reported here, together with some orientations of demographic research on mortality at oldest ages and the limits of longevity.