The process of signaling through cell surface receptors involves highly connected networks of interacting components. I will focus on the application of mathematical models to understanding signaling through immune recognition receptors which trigger a variety of immune responses. Simple models, like kinetic proofreading and serial engagement, which ignore the details of the signaling machinery, have provided considerable insight into how ligand-receptor binding properties affect signaling outcomes but are unable to make contact with the vast majority of cell signaling data. After reviewing these models and discussing their strengths and weaknesses, I will look at the problems that the modeler is confronted with when he or she tries to deal with the details of a signaling cascade. I illustrate with a model for the early signaling events mediated by the high affinity receptor for IgE, Fc eRI, a receptor that plays a key role in allergic reactions.