Following the pioneering work of Rahman (JCP 1966), Voronoi tessellations are nowadays increasingly used to analyse the microscopic fluid or granular structures, as they characterize unambiguously the geometry of the particles neighborhood. The Voronoi tessellations happened to be particularly relevant for the study of the glass transition, where local activated events preempt the relaxational dynamics at low enough temperature. To this end, one studied new conserved and geometry-based microscopic fields, which proved to correlate significantly to the potential energy landscape, the features of which increasingly determine the relaxations when the temperature is lowered. In a second part, I will show that the Voronoi and Voronoi-Laguerre tessellations can be used to define a new class of fluids, which have interesting new properties : anomalous thermodynamic scaling, zero-separation theorem, etc... I will present some recent results on the properties of a glass-forming version of such a "Voronoi liquid", which can be viewed as a new tool to probe the glass transition theories, complementing the usual 2-body potential based models.