  The Fermi-LAT telescope has measured the extragalactic gamma-ray background
(EGB) generated by the ensemble of all extragalactic sources. The energy
distribution of the EGB is well described as a power-law with a spectral index
approximately equal to 2.3, and an exponential cutoff, that is consistent with
being the effect of absorption of high energy photons assuming an emission that
is an unbroken power-law spectrum. The observations of the Fermi telescope have
also resolved the EGB, determining that most of it is formed by the sum of the
contributions of Active Galactic Nuclei (AGN) of the blazar class. The spectra
of the individual AGN sources have a broad range of spectral shapes, and the
brightest and most precisely measured sources have curved spectra that can be
fitted with the "log-parabola" (or log-normal) form. It might appear surprising
that the sum of contributions with different spectral shapes generate a
spectrum that has a simple power-law form. We suggest that this fact reveals
some important properties for the ensemble of the extragalactic sources, and
indicates that the blazar high energy emission can be considered as a "critical
phenomenon". A curved log--parabola (log-normal) form is also required to fit
the spectra of many Galactic gamma-ray sources, including the emission from the
brightest supernova remnants (SNR), and an intriguing possibility is that also
the Galactic cosmic rays are injected in interstellar space by their sources
not with a single universal power-law spectrum, as predicted by the commonly
accepted models, but instead with a broad range of spectral shapes.
