Signaling pathways come together to form networks that connect receptors to many different cellular machines. Such networks not only receive and transmit signals but also process information. The complexity of these networks requires the use of computational models to understand how information is processed and how input - output relationships are determined. Two major computational approaches used to study signaling networks are graph theory and dynamical modeling. Both approaches are useful; network analysis (application of graph theory) helps us understand how the signaling network is organized and what its information-processing capabilities are, whereas dynamical modeling helps us determine how the system changes in time and space upon receiving stimuli. Computational models have helped us identify a number of emergent properties that signaling networks possess. Such properties include ultrasensitivity, bistability, robustness, and noise-filtering capabilities. These properties endow cell-signaling networks with the ability to ignore small or transient signals and/or amplify signals to drive cellular machines that spawn numerous physiological functions associated with different cell states.