  After more than 40 years from their discovery, the long-lasting tension
between predictions and observations of GRBs prompt emission spectra starts to
be solved. We found that the observed spectra can be produced by the
synchrotron process, if the emitting particles do not completely cool. Evidence
for incomplete cooling was recently found in Swift GRBs spectra with prompt
observations down to 0.5 keV (Oganesyan et al. 2017, 2018), characterized by an
additional low-energy break. In order to search for this break at higher
energies, we analysed the 10 long and 10 short brightest GRBs detected by the
Fermi satellite in over 10 years of activity. We found that in 8/10 long GRBs
there is compelling evidence of a low energy break (below the peak energy) and
the photon indices below and above that break are remarkably consistent with
the values predicted by the synchrotron spectrum (-2/3 and -3/2, respectively).
None of the ten short GRBs analysed shows a break, but the low energy spectral
slope is consistent with -2/3. Within the framework of the GRB standard model,
these results imply a very low magnetic field in the emission region, at odds
with expectations. I also present the spectral evolution of GRB 190114C, the
first GRB detected with high significance by the MAGIC Telescopes, which shows
the compresence (in the keV-MeV energy range) of the prompt and of the
afterglow emission, the latter rising and dominating the high energy part of
the spectral energy range.
