This open access paper is a good resource if you happen to want a list of references to the mainstream scientific discussion of the past twenty years regarding trends in human life expectancy, and the predicted future of those trends. It is somewhat myopic beyond that in the sense that it gives little credit to the idea that the trend might continue or increase, as a result of future technological progress in medicine. The trend is an artifact of human efforts, and as such the size of the trend is entirely dependent on how well medicine can be made to address the causes of aging.
In the past, no effort at all was directed towards treating the causes of aging, and the small degree of extended healthy life with each passing year was an entirely accidental benefit. We are now at a point in time in which the scientific community is transitioning into making deliberate efforts to treat the causes of aging, with increasing enthusiasm and funding. Therefore expecting the future trend to look like the past trend, or even slow down, or thinking that we are in any way approaching a limit to human life span, appears to me to be a nonsensical position. We can understand why human life span is limited today, and why it was limited in the past: it does not follow that it will be limited in the future, because medical science will address the biological mechanisms involved, the accumulation of cell and tissue damage that causes aging.
How long can we live? How fast can we run or swim? Demographers disagree about the lifespan trend and its potential limit, while sports scientists discuss the frontiers of maximal physical performance. Such questions stimulate large and passionate debates about the potential of Homo sapiens and its biological upper limits. Historical series, defined as the measurable data collected since the nineteenth century for lifespan, sport, or height provide crucial information to understand human physiology and the form and nature of our progression over the last 10 generations.
Recent studies about lifespan trends increased interest about the possible ceilings in longevity for humans. This long-lasting debate increased in strength at the beginning of the 1990s. Using biological and evolutionary arguments, the first leading opinion postulated an upper limit for life expectancy at birth and maximal longevity. These limits may have already been approached: around 85-95 years for life-expectancy and 115-125 years for maximal longevity, as a result of nutritional, medical, societal, and technological progress. A second school of thought considered that life expectancy may continue to progress indefinitely at a pace of 2 to 3 added years per decade. They claim that most of the babies born during the 2000s, "if the present yearly growth in life expectancy continues through the twenty-first century," will celebrate their 100th birthday or, potentially reach physical immortality due to undefined scientific breakthroughs.
Human life-expectancy and maximal lifespan trends provide long historical series. Similar to sport achievements, though somewhat less precisely measured, it followed an unprecedented progression during the twentieth century supported by major nutritional, scientific, technological, societal, and medical innovations. From 1900 to 2000 in the majority of high-income countries, life expectancy at birth increased by ~30 years, mostly due to a reduction of child mortality through nutrition, hygiene, vaccination, and other medical improvements.
Concerning the future, trends oscillate, from pessimistic to optimistic views, but recent data suggest a slow-down in the progress of life-expectancy related to the stabilization of a very low level of infant mortality (0.2-1% of births in the healthiest countries in the world). The present slow progress in high-income countries is mostly due to reduced mortality rates of chronic non-communicable diseases, principally among cardiovascular diseases and cancers. However, those advancements have a much lower impact on life-expectancy as compared to vaccination campaigns.
Predicting a continuous linear growth of life-expectancy in the long term may probably not be relevant if the major progresses have already been accomplished. Beyond the fittest mathematical model for estimating future trends, we need to carefully examine the consistency with structural and functional limits determining maximal lifespan related to life-history strategies and evolutionary and environmental constraints. For example, aging is an irreversible process: it is complex as it concerns all physiological functions, organs, and maintenance systems. But, it also has universal characteristics, showing a continuous exponential decline starting in the third decade for all maximal indicators with an accelerated loss of physical performance until death. No escape from decline is observed, despite the best efforts of the oldest old.
Similarly, maximal lifespan increased slightly during the last two centuries, but since 1997, nobody has lived for more than 120 years. Surpassing mathematical models, projecting 300 years into the future without biological considerations, most recent data showed evidence of a lifespan plateau around 115-120 years, despite a sharp increase in the number of centenarians and supercentenarians. Jeanne Calment with 122.4 years has certainly come close to the potential biological limit of our species in term of longevity, at the benefit of an extremely rare long-lived phenotype supported by a specific lifestyle and chance.