Stochastic and spatial aspects are becoming increasingly recognized as an important factor in T-cell activation. Activation occurs in an intrinsically noisy environment, requiring only a handful of agonist peptide-major histocompatibility complex molecules, thus making consideration of signal to noise of prime importance in understanding sensitivity and specificity. Furthermore, it is widely established that surface-bound ligands are more effective at activation than soluble forms, while surface patternation has highlighted the role of spatial relocation in activation. Here we consider the results of a number of models of T-cell activation, from a realistic model of kinetic segregation-induced T-cell receptor (TCR) triggering through to simple queuing theory models. These studies highlight the constraints on cell activation by a surface receptor that recruits kinases. Our analysis shows that TCR triggering based on trapping of bound TCRs in regions of close proximity that exclude large ectodomain-containing molecules, such as the phosphatases CD45 and CD148, can effectively reproduce known signaling characteristics and is a viable 'signal transduction' mechanism distinct from oligomerization and conformation-based mechanisms. A queuing theory analysis shows the interrelation between sensitivity and specificity, emphasizing that these are properties of individual cell functions and need not be, nor are likely to be, uniform across different functions. In fact, threshold-based mechanisms of detection are shown to be poor at ligand discrimination because, although they can be highly specific, that specificity is limited to a small range of peptide densities. Time integration mechanisms however are able to control noise effectively, while kinetic proofreading mechanisms endow them with good specificity properties. Thus, threshold mechanisms are likely to be important for rapidly detecting minimal signaling requirements, thus achieving efficient scanning of antigen-presenting cells. However, for good specificity, time integration on a scale of hours is required.