  We study the effects of inhomogeneities on the evolution of the Universe, by
considering a range of cosmological models with discretized matter content.
This is done using exact and fully relativistic methods that exploit the
symmetries in and about submanifolds of spacetimes that themselves possess no
continuous global symmetries. These methods allow us to follow the evolution of
our models throughout their entire history, far beyond what has previously been
possible. We find that while some space-like curves collapse to anisotropic
singularities in finite time, others remain non-singular forever. The resulting
picture is of a cosmological spacetime in which some behaviour remains close to
Friedmann-like, while other behaviours deviate radically. In particular, we
find that large-scale acceleration is possible without any violation of the
energy conditions.
