In the last 30 years, many of the mechanisms behind signal transduction, the process by which the cell takes extracellular signals as an input and converts them to a specific cellular phenotype, have been experimentally determined. With these discoveries, however, has come the realization that the architecture of signal transduction, the signaling network, is incredibly complex. Although the main pathways between receptor and output are well-known, there is a complex net of regulatory features that include crosstalk between different pathways, spatial and temporal effects, and positive and negative feedbacks. Hence, modeling approaches have been used to try and unravel some of these complexities. We use the mitogen-activated protein kinase cascade to illustrate chemical kinetic and logic approaches to modeling signaling networks. By using a common well-known model, we illustrate here the assumptions and level of detail behind each modeling approach, which serves as an introduction to the more detailed discussions of each in the accompanying chapters in this book.