  The gamma-ray burst GRB 180720B is very peculiar. On one hand, some
interesting features have been found by performing the detailed time-resolved
spectral analysis in the prompt phase. First, the `flux-tracking' pattern is
exhibited both for the low energy spectral index $\alpha$ and the peak energy
$E_{p}$ in the Band function. Second, some parameter relations show strong
monotonous positive correlations, include $E_{p}-F$, $\alpha-F$,
$E_{p}-\alpha$, and $E_{p}-L_{\gamma,iso}$ for all time-resolved spectra.
Lastly, it should be noted that the values of $\alpha$ do not exceed the
synchrotron limits (from $-\frac{3}{2}$ to $-\frac{2}{3}$). On the other hand,
the photons with the energy of $\gtrsim$ 100 MeV were detected by LAT both in
the prompt phase and afterglow. Notably, the 5 GeV photon was observed at 142 s
after the GBM trigger. The spectrum of this burst in the LAT range can be
described as $F_{\nu}\propto \nu^{-1.3} t^{-1.54\pm0.02}$ in the afterglow
phase. And there are six GeV photons during the X-ray flare when the lower
energy emission is fading to a weaker level. We try to give reasonable
interpretations of the mechanism for prompt emission and the high energy
emission (100 MeV to GeV) in the afterglow. The interpretations suggesting that
synchrotron origin can account for the prompt emission and synchrotron
self-Compton radiation can account for both the spectrum and temporal behavior
of the 100 MeV to GeV afterglow emission that have been accepted by us.
