One of the greatest mysteries in fundamental physics is why we observe three families of elementary particles, which are apparently identical but differ in their mass. This mystery is at the root of our own existence: the stability of atomic nuclei, as well as the structure and properties of atoms, strongly depend on the masses of the elementary particles. We know how to describe such masses within the so-called Standard Model of fundamental interactions, but we do not have a rational principle which is able to explain their peculiar values. The purpose of this project is to shed light on this fascinating problem. We pursue this goal following a twofold path: on the one hand, our group exploits the potential of high-precision measurements of rare processes, which in the last few years started to hint at deviations from the Standard Model predictions; on the other hand, we try to match these observations with the theoretical development of new models that extend the current paradigm of fundamental interactions.