  The problems of the intermediate-range atomic structure of glasses and of the
mechanism for the glass transition are approached from the low-temperature end
in terms of a scenario for the atomic organization that justifies the use of an
extended tunneling model. The latter is crucial for the explanation of the
magnetic and compositional effects discovered in non-metallic glasses in the
Kelvin and milli-Kelvin temperature range. The model relies on the existence of
multi-welled local potentials for the effective tunneling particles that are a
manifestation of a non-homogeneous atomic structure deriving from the
established dynamical heterogeneities that characterize the supercooled liquid
state. It is shown that the extended tunneling model can successfully explain a
range of experiments at low temperatures, but the proposed non-homogeneous
atomic structure scenario is then tested in the light of available high
resolution electron microscopy imaging of the structure of some glasses and on
the behaviour near the transition.
