A gamma-ray burst (GRB) is a strong and fast gamma-ray emission from the explosion of stellar systems (massive stars or coalescing binary compact stellar remnants), happening at any possible redshift, and detected by space missions. Although GRBs are the most energetic events after the Big Bang, systematic search (started after the first localization in 1997) led to only 374 spectroscopic redshift measurements. For less than half, the host galaxy is detected and studied in some detail. Despite the small number of known hosts, their impact on our understanding of galaxy formation and evolution is immense. These galaxies offer the opportunity to explore regions which are observationally hostile, due to the presence of gas and dust, or the large distances reached. The typical long-duration GRB host galaxy at low redshift is small, star-forming and metal poor, whereas, at intermediate redshift, many hosts are massive, dusty and chemically evolved. Going even farther in the past of the Universe, at z > 5, long-GRB hosts have never been identified, even with the deepest NIR space observations, meaning that these galaxies are very small (stellar mass < 10^7 M_sun). We considered the possibility that some high-z GRBs occurred in primordial globular clusters, systems that evolved drastically since the beginning, but would have back then the characteristics necessary to host a GRB. At that time, the fraction of stellar mass contained in proto globular clusters might have been orders of magnitude higher than today. Plus, these objects contained in the past many massive fast rotating binary systems, which are also regarded as a favorable situation for GRBs. The common factor for all long GRBs at any redshift is the stellar progenitor: it is a very massive rare/short-lived star, present in young regions, whose redshift evolution is closely related to the star-formation history of the Universe.
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