T cells are activated when extracellular stimuli, such as a ligand binding to the T cell receptor, are converted into functional outputs by the T cell signalling network. T cell receptor signalling is a highly complex, stochastic and dynamic process involving many interacting proteins. This complexity often confounds intuition, making it difficult to develop mechanistic principles that underly experimental observations. In this Review, we describe how computational approaches can partner successfully with biological experimentation to help address this challenge, and we illustrate this paradigm by summarizing recent work that shows new aspects of the T cell signalling network.