During its division cycle, a cell replicates all its components and divides them more or less evenly between two daughter cells, so that each daughter inherits the machinery and information necessary to repeat the process. In eukaryotes, the genome is accurately replicated during a distinct phase of the cell cycle (called the S phase, for DNA synthesis), and the sister DNA molecules are carefully separated in a later phase of the cycle (M phase, for mitosis). The timing of S and M phases is controlled by a complex network of biochemical reactions, based on cyclin-dependent kinases and their associated proteins. In this chapter we analyze the simplest case of cell cycle control, the meiotic and mitotic cycles of frog eggs, to illustrate how computational models can make connections between molecular mechanisms and the physiological properties of a cell. The mechanism of this "simple" case is already so complex that informal biochemical intuition cannot reliably deduce how it works. Our intuition must be supplemented by precise mathematical and computational tools. To this end, we convert the mechanism of cell cycle control into differential equations and show how the dynamic properties of the control system (e.g., stable steady-state or oscillation) can be manipulated by changing parameter values. In this way, cell cycle control can be switched from an embryonic pattern (S-M) to a somatic pattern (G1-S-G2-M), by changing levels of gene expression. This theme (gene expression ? system dynamics ?