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Gamma-ray bursts are the most powerful explosions in the universe and aremainly 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 otherastronomical objects, such as black holes, supernovae, neutron stars, etc.,discussing in detail gamma-ray burst progenitors. We classify long and shortgamma-ray bursts, working out their timescales, and introduce the standardfireball model. Afterwards, we focus on direct applications of gamma-ray burststo cosmology and underline under which conditions such sources would act asperfect standard candles if correlations between photometric and spectroscopicproperties were not jeopardized by the \emph{circularity problem}. In thisrespect, we underline how the shortage of low-$z$ gamma-ray bursts preventsanchor gamma-ray bursts with primary distance indicators. Moreover, we analyzein detail the most adopted gamma-ray burst correlations, highlighting theirmain differences. We therefore show calibration techniques, comparing suchtreatments with non-calibration scenarios. For completeness, we discuss thephysical properties of the correlation scatters and systematics occurringduring experimental computations. Finally, we develop the most recentstatistical methods, star formation rate and high-redshift gamma-ray burstexcess and show the most recent constraints got from experimental analyses.

A roadmap to gamma-ray bursts: new developments and applications to cosmology