Scaling in the Universe

The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the Universe, I will mainly concentrate on those methods which reveal remarkable regularities and scaling in the structure of the Universe. Although in most cases I prefer not to enter into the technical aspects of how implementing such methods, more details will be furnishes about the description of galaxy clustering in terms of fractal concepts. Despite recent claims for a Universe, which behaves like a fractal at arbitrarily large scales, I will show that the fractal language can be usefully employed to disprove this picture. The emerging scenario is that of a Universe, which behaves like a self-similar structure at small scales, where fractality is dynamically generated by non-linear gravitational clustering, while preserving large-scale homogeneity. Nevertheless, even at scales $\magcir 10\hm$, where gravity still acts linearly, the distribution of galaxy clusters shows remarkable scale-invariant features, which could give precise hints about the initial conditions for the evolution of the large-scale structure of the Universe.