  We discuss the relaxation dynamics of a simple lattice gas model for
glass-forming systems and show that with increasing density of particles this
dynamics slows down very quickly. By monitoring the trajectory of tagged
particles we find that their motion is very heterogeneous in space and time,
leading to regions in space in which there is a fast dynamics and others in
which it is slow. We determine how the geometric properties of these quickly
relaxing regions depend on density and time. Motivated by this heterogeneous
hopping dynamics, we use a simple model, a variant of a continuous time random
walk, to characterize the relaxation dynamics. In particular we find from this
model that for large displacements the self part of the van Hove function shows
an exponential tail, in agreement with recent findings from experiments and
simulations of glass-forming systems.
