In this article, the origin of the concepts involved in the study of human longevity are reviewed in their historical context. The emergence of the scientific definitions and terms associated with the topic are described. Then, the different longevity's indicators (median, mean, modal age at death, Life expectancy at birth (LE), age reached by 10% of the newborns (L(10)), Highest Age Providing at Least 30 deaths (HAPaL30) and Maximum Reported Age at Death (MRAD)) and their dynamics over time are illustrated, compared and discussed with data and projection from France, with some hints on why the future can be different from the forecasts.