The Notch–Delta signal transduction pathway is critical for many processes in development and disease, with a particular role in generating distinct cell fates among groups of initially equivalent cells and sharply defining neighbouring regions in developing tissues. Recent research has provided an increasingly comprehensive list of components and molecular interactions underlying Notch signalling, without revealing how these two proteins lead to clear cell-fate decisions. Sprinzak et al. use quantitative time-lapse microscopy to show that Notch levels in a given cell are ultrasensitive to the amount of Delta present at the surface of the same cell — as opposed to that exposed by its neighbours. This abrupt molecular switch means that a cell becomes exclusively a sender of Delta signalling (with high Delta and low Notch) or a receiver (vice versa). Numerical modelling shows how this new design principle enhances the sharpness of developmental boundaries set by classical lateral inhibition. Notch and Delta are transmembrane proteins that allow neighbouring cells to communicate during development. Here, quantitative time-lapse microscopy has been used to show that the response of Notch to Delta on a neighbouring cell is graded, whereas its response to Delta on the same cell is sharp and occurs at a fixed threshold. A mathematical model explores how this new design principle enhances the sharpness of developmental boundaries set by classical lateral inhibition. The Notch–Delta signalling pathway allows communication between neighbouring cells during development1. It has a critical role in the formation of ‘fine-grained’ patterns, generating distinct cell fates among groups of initially equivalent neighbouring cells and sharply delineating neighbouring regions in developing tissues2,3,4,5. The Delta ligand has been shown to have two activities: it transactivates Notch in neighbouring cells and cis-inhibits Notch in its own cell. However, it remains unclear how Notch integrates these two activities and how the resulting system facilitates pattern formation. Here we report the development of a quantitative time-lapse microscopy platform for analysing Notch–Delta signalling dynamics in individual mammalian cells, with the aim of addressing these issues. By controlling both cis- and trans-Delta concentrations, and monitoring the dynamics of a Notch reporter, we measured the combined cis–trans input–output relationship in the Notch–Delta system. The data revealed a striking difference between the responses of Notch to trans- and cis-Delta: whereas the response to trans-Delta is graded, the response to cis-Delta is sharp and occurs at a fixed threshold, independent of trans-Delta. We developed a simple mathematical model that shows how these behaviours emerge from the mutual inactivation of Notch and Delta proteins in the same cell. This interaction generates an ultrasensitive switch between mutually exclusive sending (high Delta/low Notch) and receiving (high Notch/low Delta) signalling states. At the multicellular level, this switch can amplify small differences between neighbouring cells even without transcription-mediated feedback. This Notch–Delta signalling switch facilitates the formation of sharp boundaries and lateral-inhibition patterns in models of development, and provides insight into previously unexplained mutant behaviours.