Under cooling, a supercooled liquid undergoes a glass transition and stops flowing. Physicists do not agree on the microscopic reasons that make a glass solid. Some view this phenomenon as being collective in nature: it may be a signature of a thermodynamic phase transition, or  being caused by kinetic constraints (where particles seek to solve a sort of Chinese puzzle). Others view it as simply reflecting elementary barriers for rearrangements, controlled by the elasticity of the material. Here I will focus on  polydisperse numerical glasses, which are receiving a considerable attention, because they can be equilibrated as efficiently as experimental molecular liquids. I will  Introduce a novel algorithm to systematically extract elementary rearrangements in a broad energy range. It allows to make, for the first time, a quantitative prediction on the relaxation time, assuming that relaxation is not collective in nature. The comparison with observation is very good. I will explain why, in such a scenario, dynamical correlations emerge even if they have little effects on the dynamics.  I will discuss the nature of elementary rearrangements under cooling, and how these aspects relate to mean field description of glasses.