Localization is a key mechanism for the emergence of non-ergodicity in disordered quantum systems. In this seminar, I will present some numerical results which suggest that quantum localization shares a close analogy with the physics of spin glasses, another paradigm of non-ergodic behavior in classical disordered systems. I will focus on the quantum transport through a disordered two-dimensional sample in the localized regime and show that it verifies several important glassy properties: pinning, avalanches and chaos. This problem is addressed by following the well-known analogy between quantum localization and the physics of directed polymers, one of the simplest model of statistical physics in which disorder plays a non-trivial role, as in spin glasses. I will first recall how to observe the dominant paths taken by the transport and demonstrate that these paths verify pinning and avalanches. Then, I will characterize the spin glass chaos property: Two infinitesimally perturbed replicas of the same sample have their correlation which vanishes at the thermodynamic limit following a characteristic single parameter scaling law.