For the most part, research in the area of cytogerontology, i.e., investigation of the mechanisms of aging in the experiments on cultured cells, is carried out using the "Hayflick's model". More than forty years have passed since the appearance of that model, and during this period of time, very much data were obtained on its basis. These data contributed significantly to our knowledge of the behavior of both animal and human cultured cells. Specifically, we already know of the mechanisms underlying the aging in vitro. On the other hand, in my opinion, little has changed in our knowledge of the aging of the whole organism. In all likelihood, this can be explained by that the Hayflick's model is, like many others used in the experimental gerontology, correlative, i.e. based on a number of detected correlations. In the case of Hayflick's model, these are correlations between the mitotic potential of cells (cell population doubling potential) and some "gerontological" parameters and indices: species life-span, donor age, evidence of progeroid syndromes, etc., as well as various changes of normal (diploid) cells during long-term cultivation and during aging of the organism. It is, however, well known that very frequently a good correlation has nothing to do with the essence (gist) of the phenomenon. For example, we do know that the amount of gray hair correlates quite well with the age of an individual but is in no way related to the mechanisms of his/her aging and probability of death. In this case, the absence of cause-effect relationships is evident, which are, at the same time, indispensable for the development of gist models. These models, as distinct from the correlative ones, are based on a certain concept of aging. In the case of Hayflick's model, such a concept is absent: we cannot explain, using the "Hayflick's limit", why our organism ages. This conclusion was convincingly confirmed by the discovery of telomere mechanism which determines the aging of cells in vitro. That discovery initiated the appearance of theories attempting to explain the process of aging in vivo also on its basis. However, it has become clear that the mechanisms of aging of the entire organism, located, apparently, in its postmitotic cells, such as neurons or cardiomyocytes, cannot be explained in the framework of this approach. Hence, we believe that it is essential to develop "gist" models of aging using cultured cells. The mechanisms of cell aging in such models should be similar to the mechanisms of cell aging in the entire organism. Our "stationary phase aging" model could be one of such models, which is based on the assumption of the leading role of cell proliferation restriction in the processes of aging. We assume that the accumulation of "senile" damage is caused by the restriction of cell proliferation either due to the formation of differentiated cell populations during development (in vivo) or to the existence of saturation density phenomenon (in vitro). Cell proliferation changes themselves do not induce aging, they only lead to the accumulation of macromolecular defects, which, in turn, lead to the deterioration of tissues, organs, and, eventually, of the entire organism, increasing the probability of its death. Within the framework of our model, we define cell aging as the accumulation in a cell population of various types of damage identical to the damage arising in senescing multicellular organism. And, finally, it is essential to determine how the cell is dying and what the death of the cell is. These definitions will help to draw real parallels between the "genuine" aging of cells (i.e., increasing probability of their death with "age") and the aging of multicellular organisms.