The existence of the upper bound of the life expectancy is still a subject of lively discussion among researchers of different disciplines (demography, actuary, genetics, biometrics, etc.). The article presents arguments for and against the existence of such maximum, and opinions concerning its value.The discussion of advantages and disadvantages of the life expectancy as a proper parameter to be used opens the paper with an emphasis on some interpretative possibilities and limitations when referring to the period and cohort life tables. Syntheses of theoretic discussions on the upper bound of longevity and estimates of it, formulated in the past, constitute two consecutive parts. Considerations on these theoretic concepts and past estimates give the impression how strongly conclusions concerning the expected maximum life expectancy are based on intuition rather than on solid scientific grounds. Improvements in mortality usually progresses faster than scientists' expectations. Currently, experts' opinions and future estimates imply that the life expectancy of 85 years for both sexes together will be exceeded up till 2050. It will question many predictions concerning mortality, and possibly give way to the new ones. The paper concludes that it seems to be better to formulate predictions concerning future trends in the life expectancy rather than make fundamental quantitative statements about its value. It is also suggested that possibly it is not the maximum life expectancy that should be considered. Maybe, it is more important to ask, whether the further lengthening of life will be accompanied by improvement of health among the old and the increase in the disability-free age.