Revisiting classical and quantum disordered systems from the unifying perspective of large deviations

The theory of large deviations is already the natural language for the statistical physics of equilibrium and non-equilibrium. In the field of disordered systems, the analysis via large deviations is even more useful to describe within a unified perspective the typical events and the rare events that occur on various scales. In the present pedagogical introduction, we revisit various emblematic classical and quantum disordered systems in order to highlight the common underlying mechanisms from the point of view of large deviations.