Intercellular communication mediated by the Notch signalling pathway plays a central role in a wide range of developmental processes. Studies in many different systems show that the dynamics of Notch signalling are markedly different in different contexts, ranging from fast approach to stable steady states, through transient fluctuations, to spatially-coordinated oscillations. In this talk, I will discuss mathematical models that can provide insight into the origins of, and relations between, these different dynamical regimes. In particular, the models give insights into the ways in which the interaction of different time scales relevant at the cellular and tissue levels can regulate patterns of cellular behaviour.