The notion of center of an object, be it a set of observations, a physical object or a random variable, is difficult to define. This motivated the development of general ways to measure centrality via depth functions. Such mappings allow for comparing relative centrality of two locations and, consequently, providing a center-outward ordering. Many such mappings have been introduced in the literature in recent decades and this is subject to intense research in, among other, nonparametric statistics and functional data analysis. In the webinar, selected statisticians will present their recent works and elaborate on different aspects of this topic. Speakers: – Dimitri Konen, Université Libre de Bruxelles (ULB), Belgium – Stanislav Nagy, Faculty of Mathematics and Physics, Charles University, Czech Republic – Pavlo Mozharovskyi, LTCI, Telecom Paris, Institut Polytechnique de Paris, France Discussant: Germain Van Bever, Université de Namur, Belgium. The webinar is part of YoungStatS project of the Young Statisticians Europe initiative (FENStatS) supported by the Bernoulli Society for Mathematical Statistics and Probability and the Institute of Mathematical Statistics (IMS).