The authors review structured cell population models. They mainly compare the branching process approach and the partial differential equations approach. First it is shown how the branching processes with continuous state space can be used to derive the authors’ basic model of cell cycle in a more rigorous manner, where a major role is played by an unsymmetric version of Fubini’s theorem for Stieltjes integrals. Then the authors show that they can as well describe the dynamics of cells in their model in terms of a partial differential equation with age and size structure, arbitrary growth function, and nonlocal boundary conditions. In the rest of this paper, a special case of the authors’ basic model is considered where the cell cycle duration is determined by the birth size of the cells.