  For several atomistic models of glass formers, at conditions below their
glassy dynamics onset temperatures, ${T_\mathrm{o}}$, we use importance
sampling of trajectory space to study the structure, statistics and dynamics of
excitations responsible for structural relaxation. Excitations are detected in
terms of persistent particle displacements of length $a$. At supercooled
conditions, for $a$ of the order of or smaller than a particle diameter, we
find that excitations are associated with correlated particle motions that are
sparse and localized, occupying a volume with an average radius that is
temperature independent and no larger than a few particle diameters. We show
that the statistics and dynamics of these excitations are facilitated and
hierarchical. Excitation energy scales grow logarithmically with $a$.
Excitations at one point in space facilitate the birth and death of excitations
at neighboring locations, and space-time excitation structures are microcosms
of heterogeneous dynamics at larger scales. This nature of dynamics becomes
increasingly dominant as temperature $T$ is lowered. We show that slowing of
dynamics upon decreasing temperature below $T_\mathrm{o}$ is the result of a
decreasing concentration of excitations and concomitant growing hierarchical
length scales, and further that the structural relaxation time $\tau$ follows
the parabolic law, $\log(\tau / \tau_\mathrm{o}) = J^2(1/T -
1/T_\mathrm{o})^2$, for $T<T_\mathrm{o}$, where $J$, $\tau_\mathrm{o}$ and
$T_\mathrm{o}$ can be predicted quantitatively from dynamics at short time
scales. Particle motion is facilitated and directional, and we show this
becomes more apparent with decreasing $T$. We show that stringlike motion is a
natural consequence of facilitated, hierarchical dynamics.
