A roadmap to gamma-ray bursts: new developments and applications to
  cosmology
  Gamma-ray bursts are the most powerful explosions in the universe and are
mainly placed at very large redshifts, up to $z\simeq 9$. In this short review,
we first discuss gamma-ray burst classification and morphological properties.
We then report the likely relations between gamma-ray bursts and other
astronomical objects, such as black holes, supernovae, neutron stars, etc.,
discussing in detail gamma-ray burst progenitors. We classify long and short
gamma-ray bursts, working out their timescales, and introduce the standard
fireball model. Afterwards, we focus on direct applications of gamma-ray bursts
to cosmology and underline under which conditions such sources would act as
perfect standard candles if correlations between photometric and spectroscopic
properties were not jeopardized by the \emph{circularity problem}. In this
respect, we underline how the shortage of low-$z$ gamma-ray bursts prevents
anchor gamma-ray bursts with primary distance indicators. Moreover, we analyze
in detail the most adopted gamma-ray burst correlations, highlighting their
main differences. We therefore show calibration techniques, comparing such
treatments with non-calibration scenarios. For completeness, we discuss the
physical properties of the correlation scatters and systematics occurring
during experimental computations. Finally, we develop the most recent
statistical methods, star formation rate and high-redshift gamma-ray burst
excess and show the most recent constraints got from experimental analyses.
