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. It is becoming more and more clear than galaxy structures are characterized by large-scale power-law correlations and the issue of the possible crossover toward homogeneity at large scale is revamping. The main statistical properties of galaxy distributions are reviewed and it is presented a discussion of the key theoretical open questions for the understating large scale structures.