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Voronoi observables, a tool to study dense assemblies of particles.
Following the pioneering work of Rahman (JCP 1966), Voronoi tessellations are nowadays increasingly used to analyse microscopic fluids or granular structures, as they characterize unambiguously the geometry of the particles neighborhood. In this talk, I will present the general properties of Voronoi tessellations, in particular their rather simple geometrical features, and the associated susceptibility properties upon displacement of particles. I will also discuss their usefulness to define related observables which can help to get a better understanding of the dynamical processes at work at the microscopic scale, particularly for glass-forming liquids where the slowing down is there the most pronounced. Finally, I will also show that the Voronoi observables can be given an active role and allow to devise new models of fluids with original properties. This point of view is particularly suited for active matter, where the interactions of an agent with its neighborhood are often preprocessed and topological, rather than pairwise and metric.