Complex networks of interacting proteins control the physiological properties of a cell (metabolism, reproduction, motility, signaling, etc.). Intuitive reasoning about these networks
is often sufficient to guide the next experiment, and a cartoon drawing of a network can be useful in codifying the results of hundreds of observations. But what tools are available for understanding the rich dynamical repertoire of such control systems? Why does a control system behave the way it does? What other behaviors are possible? How do these behaviors depend on the genetic and biochemical parameters of the system (gene dosage, enzymatic rate constants, equilibrium binding constants, etc)? Using basic principles of biochemical kinetics, network diagrams can be converted into sets of ordinary differential equations and their properties explored by analytical and computational methods. We will describe the basic ideas and tools required for this type of modeling and illustrate the approach with a variety of examples taken from modern research in cell biology (growth, division, death, signaling, rhythms, and disease).