  We review a theoretical perspective of the dynamics of glass forming liquids
and the glass transition. It is a perspective we have developed with our
collaborators during this decade. It is based upon the structure of trajectory
space. This structure emerges from spatial correlations of dynamics that appear
in disordered systems as they approach non-ergodic or jammed states. It is
characterized in terms of dynamical heterogeneity, facilitation and excitation
lines. These features are associated with a newly discovered class of
non-equilibrium phase transitions. Equilibrium properties have little if
anything to do with it. The broken symmetries of these transitions are obscure
or absent in spatial structures, but they are vivid in space-time (i.e.,
trajectory space). In our view, the glass transition is an example of this
class of transitions. The basic ideas and principles we review were originally
developed through the analysis of idealized and abstract models. Nevertheless,
the central ideas are easily illustrated with reference to molecular dynamics
of more realistic atomistic models, and we use that illustrative approach here.
