How do biochemical signaling pathways generate biological specificity? This question is fundamental to modern biology, and its enigma has been accentuated by the discovery that most proteins in signaling networks serve multifunctional roles. An answer to this question may lie in analyzing network properties rather than individual traits of proteins in order to elucidate design principles of biochemical networks that enable biological decision-making. We discuss how this is achieved in the MST2/Hippo-Raf-1 signaling network with the help of mathematical modeling and model-based analysis, which showed that competing protein interactions with affinities controlled by dynamic protein modifications can function as Boolean computing devices that determine cell fate decisions. In addition, we discuss areas of interest for future research and highlight how systems approaches would be of benefit.