During somitogenesis, presomitic mesoderm cells coordinate the patterning of somites through synchronised oscillations of Notch signalling, which create sequential waves of gene expression (phase waves) that propagate from the posterior to the anterior end of the tissue. Traditional models attribute these waves to global signals across the tissue, but increasing evidence suggests they can self-organise between cells. Here, Klepstad and Marcon propose a new theoretical framework that recreates the dynamics of mouse somitogenesis observed in vivo and in vitro. First, they establish the ‘Sevilletor’ model, a minimal equation framework combining an oscillatory reaction-diffusion system and global signals. Using the Sevilletor, they recapitulate and compare three existing somitogenesis models: the Clock and Wavefront model, the Progressive Oscillatory Reaction-Diffusion model and the Clock and Gradient model. Finally, the authors present an alternative somitogenesis model, the Clock and Wavefront Self-Organising model (CWS), which contains a self-organising region where phase waves can arise from local cell-cell coupling, independent of the global signals. Unlike other models, the CWS model can recapitulate the excitable behaviour of mouse presomitic mesoderm cells observed in vitro, which is triggered by local cell communication. Overall, this study presents a new modelling framework for understanding self-organising pattern formation in different tissues and organisms.