Self-organisation is a fascinating and challenging topic, being linked to key theoretical aspects of out-of-equilibrium physics and developmental biology and practical issues of robotics and information networks. In this talk we explore a novel approach to understand self-organization that combines tools of non-linear systems analysis and multivariate information theory. In particular, we study dynamical systems as devices that dissipate information in order to induce correlations, which in turn are responsible of emerging structures and global behaviour. Our approach is to generate a multi-layered representation of the interdependencies, which can be used to track structures in the transient and stationary regimes. We illustrate this framework by showing how it can be used to analyse self-organisation in cellular automata, and finally discuss some open questions and future lines if research.