A survey of three types of cell population models is presented in this paper. The main issue in all the surveyed works is whether or not there exists a stable type distribution (s.t.d.). In the last few years, many efforts were directed towards describing the most general models which still exhibit s.t.d. Progress made in the case of size density models are discussed. A slightly extended version of a time continous daughter cell model, studied in Arino et al. (1991), is presented. Recently, some authors have undertaken the task of comparing models of various origins and types. Such works are alluded to in a discussion.