The standard model of cosmology is based on a homogeneous and
isotropic Friedmann solution, with small perturbations accounting for
almost all structure. Such an approach inherently assumes that a
universe that has a statistically homogeneous matter content is well
modelled by a homogeneous solution of Einstein’s equations, with the
energy-momentum tensor being given by the averaged matter fields. This
seemingly innocuous statement is, however, hard to justify
mathematically. It is therefore useful to consider cosmological models
in which the matter is distributed in an inhomogeneous way from the
outset, while being statistically homogeneous on large scales, in order
to investigate its validity. In this talk I will give an outline of some
of the recent progress that has been made in this field, and discuss
what this means for the standard approach.