  The quantum excitations in glasses have long presented a set of puzzles for
condensed matter physicists. A common view is that they are largely disordered
analogs of elementary excitations in crystals, supplemented by two level
systems which are chemically local entities coming from disorder. A radical
revision of this picture argues that the excitations in low temperature glasses
are deeply connected to the energy landscape of the glass when it vitrifies:
the excitations are not low excited states built on a single ground state but
locally defined resonances, high in the energy spectrum of a solid. According
to a semiclassical analysis, the two level systems involve resonant collective
tunneling motions of around two hundred molecular units which are relics of the
mosaic of cooperative motions at the glass transition temperature $T_g$. The
density of states of the TLS is determined by $T_g$ and the mosaic's length
scale, which is a weak function of the cooling rate. The universality of phonon
scattering in insulating glasses is explained. The Boson Peak and the plateau
in thermal conductivity, observed at higher temperatures, are also
quantitatively understood within the picture as arising from the same
cooperative motions, but now accompanied by thermal activation of the mosaic's
vibrational modes. The dynamics of some of the local structural transitions
have significant quantum corrections to the semiclassical picture. These
corrections lead to a deviation of the heat capacity and conductivity from the
standard tunneling model results and explain the anomalous time dependence of
the heat capacity. Interaction between tunneling centers contributes to the
large and negative value of the Gr\"{u}neisen parameter often observed in
glasses.
