  There is a growing belief that the mode coupling theory is the proper
microscopic theory for the dynamics of the undercooled liquid above a critical
temperature T_c. In addition, there is some evidence that the system leaves the
saddlepoints of the energy landscape to settle in the valleys at this critical
temperature. Finally, there is a microscopic theory for the entropy at the
calorimetric glass transition T_g by Mezard and Parisi, which allows to
calculate the Kauzmann temperature from the atomic pair potentials.
  The dynamics of the frozen glass phase is at present limited to
phenomenological models. In the spirit of the energy landscape concept, one
considers an ensemble of independent asymmetric double-well potentials with a
wide distribution of barrier heights and asymmetries (ADWP or Gilroy-Phillips
model). The model gives an excellent description of the relaxation of glasses
up to about T_g/4. Above this temperature, the interaction between different
relaxation centers begins to play a role. One can show that the interaction
reduces the number of relaxation centers needed to bring the shear modulus down
to zero by a factor of three.
