Statistical physics for cosmic structures

Galaxy structures form a complex irregular pattern, characterized by clusters of galaxies which are organized in filaments around large voids. Recently the Sloan Digital Sky Survey project is extending our knowledge of the galaxy distribution, by discovering new and larger structures. The fractal properties are becoming more clear and well established and the issue of the possible crossover toward homogeneity at large scale is revamping. We review the main statistical properties of galaxy distributions discussing the main theoretical open question in the perspective of complex systems.