A centroidal Voronoi tessellation (CVT) is a Voronoi tessellation of a given set such that the associated generating points are centroids (centers of mass) of the corresponding Voronoi regions. It is a concept that has found interesting applications in diverse areas, well beyond simple geometric settings. In this talk, we present the basic concept of CVT and its various generalizations, along with discussions on deterministic and stochastic numerical algorithms for the construction of CVT. We also give a few illustrative examples of applications ranging from image and data analysis to numerical PDEs.