  Ideas of Statistical Physics are very relevant for cosmic structures
especially considering that the field is undergoing a period of exceptional
development with many new data appearing on a monthly basis. In the past years
we have focused mostly on galaxy distributions and their statistical
properties. This led to an interesting debate which will be resolved by the
next generation of data in a couple of years. In addition here we discuss the
statistical properties of the fluctuations of the cosmic microwave background
which are small in amplitude but complex in structure. We finally discuss the
connection between these observations and the Harrison-Zeldovich spectrum and
its further implications on the theories of structure formation and the and the
cosmological $N$-body simulations.
