Poisson-Voronoi Tessellations provide a probabilistic approach which is relevant to many questions arising from geometry. Recent work has focused on the limiting (ideal) case, where the intensity of the point cloud tends to zero. In the hyperbolic setting, the limit converges to a tessellation where tiles correspond to points on the visual boundary of hyperbolic space. This ideal Poisson-Voronoi tessellation has been used as a tool to prove significant new results, including bounds on Cheeger constants [Budzinski-Curien-Petri '22], rank gradient / fixed price [Frączyk-Mellick-Wilkens '23], and uniqueness thresholds for percolation [Grebík-Recke '25]. In this talk, I will describe the ideal Poisson-Voronoi tessellation, give an overview of recent results that use it, and outline my current research directions.