**11. Conclusions**

In this review, we outlined some of the most recent developments toward GRB physics, properties, and their applications to cosmology. In particular, the review is structured into two main parts.

In the first part, we discussed the basic demands of GRBs, including their main observable quantities, their classification scheme into LGRBs and SGRBs and the corresponding issues, emphasizing new possible ways of classification, still the object of speculation. Afterwards, we put emphasis on GRB progenitors and on their fundamental microphysics, in view of the experimental evidence characterizing prompt and afterglow emissions, etc. LGRB connections with SNe have been explored as well along with SGRB matching with KNe and GWs. Great emphasis has been devoted to portray the standard GRB formation, working with the well consolidated *fireball model*. Particle acceleration and radiative processes, predicted in such a picture, have been largely reported, with particular concern for observable signatures and the standard model frontiers. Even in this part, we illustrated that GRBs cannot be contemplated as genuine standard candles, since there is no consensus toward their internal processes that we depicted throughout the manuscript. Accordingly, their luminosity cannot be easily related to their redshifts as, for instance, one does for SNe.

For these aspects and for the overall limitations described above, we developed in the second part considerable cosmological applications of GRB physics. We tried to standardize GRBs by means of the most recent techniques and accentuated GRBs are essential to reconcile small with intermediate redshift domains, opening new scenarios toward our universe comprehension. In this respect, we featured how GRBs could be used as complementary and outstanding probes to trace dark energy's evolution in support of other indicators, e.g., SNeIa, BAO, CMB, Hubble differential data, etc. Thereby, we have shown a few statistical treatments related to Bayesian analysis in cosmology, able to combine GRBs with other catalogs of data, reporting the most recent cosmological constraints on dark energy models. To do so, we expounded the bristly circularity problem, burdening GRBs in cosmological set ups. In particular, we also changed perspective, showing how to avoid calibration, i.e., how not to employ the circularity. We confronted the two methods and checked which departures could be expected from the standard cosmological model through the use of GRBs in both of the cases. Details on error propagation and GRB systematics have been discussed for several cosmic GRB correlations. Model dependent and independent techniques of calibrations have been likewise portrayed.

Perspectives about GRB developments will be based on clarifying the overall issues raised in this review. In particular, it is of utmost importance to shed light on how to standardize GRBs, in view of a likely self-consistent evolutionary paradigm, so far missing. With this recipe, we expect in the incoming years to improve GRB use in cosmology and get rid of circularity and greatly reduce the systematics and all the other issues that affect GRB data and challenge their use in cosmology. In particular, some models akin to those characterizing other cosmic indicators will spell out how to describe in toto GRB physics and evolution.

**Author Contributions:** Conceptualization, O.L. and M.M.; methodology, O.L. and M.M.; software, O.L. and M.M.; validation, O.L. and M.M.; formal analysis, O.L. and M.M.; investigation, O.L. and M.M.; resources, O.L. and M.M.; data curation, O.L. and M.M.; writing—original draft preparation, O.L. and M.M.; writing—review and editing, O.L. and M.M.; visualization, O.L. and M.M.; supervision, O.L. and M.M.; project administration, O.L. and M.M.; funding acquisition, O.L. and M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** O.L. and M.M. acknowledge partial support of the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. IRN AP08052311. M. M. is supported by INFN as part of the MoonLIGHT-2 experiment in the framework of the research activities of CSN2.

**Data Availability Statement:** Data are taken from the papers quoted in the text.

**Acknowledgments:** We acknowledge the financial support provided by the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. IRN AP08052311.

**Conflicts of Interest:** The authors declare no conflict of interest.
