The data collected by the Fermi Large Area Telescope (LAT) for more than four years enable a huge step forward in measuring and understanding the origins of the extragalactic diffuse gamma-ray background (EGB). The EGB originates from the superposition of different populations of unresolved sources with possible contributions from genuinely diffuse and exotic processes. In most parts of the sky it is sub-dominant to the Galactic diffuse emission, which represents a foreground to be subtracted to allow a measurement of the EGB intensity. Due to the long exposure, an improved event selection, better understanding of the Galactic diffuse foregrounds and the charged particle backgrounds, we can now extend the measurement of the spectrum of the EGB to the energy range between 200 MeV and several hundred GeV. Furthermore, population studies based on resolved LAT sources allow to constrain the contribution of individual classes of unresolved sources to the EGB.