The extreme luminosity of gamma-ray bursts and their afterglows means they are detectable, in principle, to very high redshifts. Although the redshift distribution of gamma-ray bursts (GRBs) is difficult to determine, due to incompleteness of present samples, we argue that for Swift-detected bursts, the median redshift is between 2.5 and 3, with a few per cent probably at z>6. Thus, GRBs are potentially powerful probes of the era of reionization and the sources responsible for it. Moreover, it seems probable that they can provide constraints on the star-formation history of the Universe and may also help in the determination of the cosmological parameters.