The magnetized universe

Cosmology, high-energy physics and astrophysics are today converging to the study of large scale magnetic fields. While the experimental evidence for the existence of large scale magnetization in galaxies, clusters and super-clusters is rather compelling, the origin of the phenomenon remains puzzling especially in light, of the most recent observations. The purpose of the present review is to describe the physical motivations and the open theoretical problems related to the existence of large scale magnetic fields.