The origin of the Fermi-LAT $\gamma$-ray background

The origin of the Isotropic Diffuse $\gamma$-Ray Background (IGRB) is one of the most intriguing mystery in astrophysics. Recently the Large Area Telescope (LAT) on board the Fermi Gamma-Ray Space Telescope has measured the IGRB spectrum from 100 MeV to 820 GeV. Thousands of extragalactic sources are detected at $\gamma$-ray energies and, thanks to Fermi-LAT catalogs and to population studies, we show that the IGRB can be explained, in the entire energy range, by the $\gamma$-ray emission from unresolved misaligned Active Galactic Nuclei, blazars and Star Forming Galaxies. Finally we derive, with a dedicated analysis based on the 2FHL Fermi-LAT catalog at $E>50$ GeV, the intrinsic source count distribution of blazars and demonstrate that this source population explains the $86^{+16}_{-14}\%$ of the total extragalactic $\gamma$-ray background.