  The question of the nature of galaxy clustering and the possible homogeneity
of galaxy distribution is one of the fundamental problem of cosmology. It is
well established that galaxy structures are characterized, up to a certain
scale, by fractal properties. The possible crossover to homogeneity is instead
still matter of debate. However, independently on the specific value of the
homogeneity scale, the fractal nature of galaxy clustering requires new methods
and theoretical concepts developed in the area of statistical physics and
complexity. In this lecture we discuss a new perspective on the problem of
cosmological structures formation, both from the experimental and the
theoretical points of view. This new perspective leads to a very interesting
and constructive interaction between the fields of cosmic structures,
statistical physics and complexity with very challenging open problems which we
also discuss.
