While the nature of the short and long-range structure of glasses was clarified, the medium-range (MR) structure of glasses is still a matter of debate. On the other hand, the magnetism of ordinary insulating glasses was considered as made up of Larmor diamagnetism and Langevin paramagnetism of the atomic impurities (Fe). The seminar will prove that a novel type of paramagnetism is to be found in glasses that is intrinsic to the glassy nature of the structure of these solids. This is revealed through the temperature (T) and magnetic field (H) dependence of the bulk magnetisation (M), once Larmor and Langevin contributions are carefully subtracted out. The remaining, intrinsic part of the magnetisation displays a peculiar behaviour in all the samples that were studied and does not have a known standard explanation. The explanation offered in this talk is that the MR-structure of glasses should be thought of as made up of jam-packed solid-like nanometric cells with no crystallinity in the bulk and liquid-like atomic species in the voids between the cells. Electronic tunneling takes place in a local three-welled potential due to this structure and the model can successfully reproduce all the observed behaviour of the measured M(T,H).