The overwhelming majority of research in the field of cytogerontology (i.e. investigating mechanisms of aging in experiments with cultured cells) has been done using the widely applied Hayflick's model. More than 40 years have passed since the appearance of the model, and during this time numerous data were obtained on its basis. The data significantly contributed to our knowledge of the behavior of cultured animal and human cells. In particular, we know enough about the in vitro aging phenomenon. But in my opinion, little has changed in our knowledge of aging in the whole organism. This may be, presumably, because Hayflich's model, like many other models used in experimental gerontology, is correlative, i.e. based on a great variety of detected correlations. In Hayflick's model these are correlations between the cell mitotic potential (cell population doubling potential) and the number of "gerontological" parameters and indices, such as the species life span, donor's age, evidence of progeroid syndromes, etc, and also correlations between various changes of normal (diploid) cells during a long-term cultivation and in the course of organismal aging. However, it is well known that a good correlation does not frequently have anything in common with the essence (gist) of the phenomenon under investigation. For example, the amount of grey hair in the individual is known to excellently correlate with his or her age, being, however, in no way associated with mechanisms of aging or probability of death. In this case, the absence of cause-effect relationships is evident. But it is these particular relationships that are totally indispensable for gist models developing. Such models, different from the correlative ones, are based on a definite concept of aging phenomenon. With the Hayflick's model, such a concept is absent, since using "Hayflick's limit" one cannot explain why the human organism is aging eventually. This can be exemplified by a discovery of a telomere mechanism, which is claimed to determine cell aging in vitro. This discovery triggered an outburst of theories aimed to explain on its basis as well the process of aging in vivo. However, now it is clear that mechanisms of the whole organism aging, hidden, presumably, in its postmitotic cells (neurons or cardiomyocytes) cannot be accounted for by this approach. In view of all stated above, we consider as indispensable the elaboration of "gist" models of aging using cultured cells. Mechanism of cell aging in these models must be similar to those in the whole organism. We believe that one of such models may be our "stationary phase aging" model, based on an assumption of the leading role of cell proliferation restriction in aging. We assume that accumulation of "senile" damage may by caused by the restriction of cell proliferation due to both the formation of differentiated cell populations in the course of development, and the existence of saturation density phenomenon (in vitro). Cell proliferation changes by themselves do not induce any aging processes, but lead only to accumulating macromolecular defects, which in their turn generate deterioration of tissues, organs, and eventually of the whole organism, thus increasing the probability of its death. Within the framework of our model, we define cell aging as the accumulation in a cell population of different types of damage identical to the damage arising in senscencing multicellular organism. And finally, we consider as very important the future studies aimed to determine the process of cell dying and cell death in general. Availability of such definitions would help to draw real parallels between the "genuine" cell aging (i.e. the increased probability of cell destruction with "age") and aging of the multicellular organism.