Standard models of cosmology treat fluctuations as very small amplitude perturbations for which the most noticeable feature is super-homogeneity. This is a property that is supposed to be satisfied by matter fluctuations in all standard theoretical models of structure formation, such as LCDM and its variants. This is a global condition on the correlation properties
of the matter density field, which can be understood as a consistency constraint in the framework of FRW cosmology, and it corresponds to a very fine tuned balance between negative and positive correlations of density
fluctuations and to the fastest possible decay of the normalized mass variance
on large scales. On the other hand, deeper and more accurate galaxy surveys have allowed us to
study larger and larger volumes of space: the number of redshifts is
grown by a factor 1000 in the last twenty years. By
studying the probability density function of conditional fluctuations in
the newest three dimensional galaxy samples, we found that large scale
structures are quite typical and correspond to large fluctuations in the
matter density field up to the largest scales probed by the available
samples. Such galaxy structures seem to be too large in amplitude and too
extended in space to be compatible with standard models of galaxy
formation. While the observed inhomogeneities pose a fundamental challenge to the standard picture
of cosmology they also represent an important opportunity which may open new
directions for many cosmological puzzles.