When cooled down below their melting temperature, liquids undergo a phase transition to a stable crystalline state, where atoms rearrange in a periodic fashion in order to form a long range order. For some liquids however, when the cooling is fast enough, crystallization can be avoided and the system progressively enters a metastable state termed « supercooled ». In this regime, the dynamics of the liquid becomes more and more heterogeneous and the viscosity increases dramatically as the temperature is reduced, to the point where the system stops flowing and solidifies, it turns into glass. Despite this sudden ridigity, it keeps the properties of a liquid at the microscopic scale, with a disordered -or « amorphous »- structure, that contrasts with its stable crystalline phase. The theoretical origin of this glass transition remains enigmatic, in particular the process in which viscosity increases so strikingly by progressively trapping the system in a metastable state instead of crystallizing. This surprising phenomenon is the subject of intensive research, and a number of theories still attempt to explain its origin through thermodynamic, dynamic or simply structural mechanisms. In this thesis, we focus on structural aspects by proposing to study the local structure of numerical model glass formers. In particular, we develop a method for community inference, based on information theory, that allows to reveal the structural heterogeneity in these systems using simple spatial correlations. This method is based on the concept of « clustering », an unsupervised learning framework that consists in grouping the particles of a system into communities depending on the properties of their local structure. Secondly, we put community inference into perspective with other clustering methods, leading notably to the publication of a versatile open source code dedicated to the study of local structure in supercooled liquids and glasses. We then show that, to some extent, these structural communities are correlated to the dynamic heterogeneities that are characteristic of supercooled liquids. Finally, thanks to recent advances in the domains of computer simulations, we study the evolution of the structure and of the dynamics in a ternary model supercooled liquid through a very wide range of temperatures. These simulations allow us to test various theoretical predictions for the glass transition with an unprecedented precision compared to conventional simulations.