CentroidalVoronoitessellations(CVTs)havebecomeausefultoolinmanyapplicationsrangingfromgeometricmodeling,imageanddataanalysis,andnumericalpartialdifferentialequations,toproblemsinphysics,astrophysics,chemistry,andbiology.Inthispaper,webrieflyreviewtheCVTconceptandafewofitsgeneralizationsandwell-knownproperties.WethenpresentanoverviewofrecentadvancesinbothmathematicalandcomputationalstudiesandinpracticalapplicationsofCVTs.Wheneverpossible,wepointoutsomeoutstandingissuesthatstillneedinvestigating.