Does the human lifespan have an impenetrable biological upper limit which ultimately will stop further increase in life lengths? Answers to this question are important for our understanding of the ageing process, and for the organization of society, and have led to intense controversies. Demographic data for  humans have been interpreted as showing existence of a limit  close to the age, 122.45 years, of the  longest living documented human, Jeanne Calment, or even as indication of a decreasing limit, but also as evidence that a limit does not exist. This talk uses EVS, extreme value statistics, to study what data says about human mortality after age 110. We show that in north America, western Europe, and Japan the yearly probability of dying after age 110 is constant and about 53 % per year.  Hence there is no finite limit to the human lifespan. Still, given the present stage of biotechnology, it is unlikely that during the next 25 years anyone will live longer than 128 years in these countries. Data, remarkably, show  little  difference in mortality  after age 110 between men and women, between earlier and later periods, between ages, or between persons with different lifestyles or genetic backgrounds. These results can help testing biological theories of aging and aid early confirmation of success of efforts to find a cure for ageing. This is joint work with Dmitrii Zholud.