Gamma-ray bursts (GRBs) are the most luminous electromagnetic explosions in the Universe, which emit up to $8.8\times10^{54}$ erg isotropic equivalent energy in the hard X-ray band. The high luminosity makes them detectable out to the largest distances yet explored in the Universe. GRBs, as bright beacons in the deep Universe, would be the ideal tool to probe the properties of high-redshift universe: including the cosmic expansion and dark energy, star formation rate, the reionization epoch and the metal enrichment history of the Universe. In this article, we review the luminosity correlations of GRBs, and implications for constraining the cosmological parameters and dark energy. Observations show that the progenitors of long GRBs are massive stars. So it is expected that long GRBs are tracers of star formation rate. We also review the high-redshift star formation rate derived from GRBs, and implications for the cosmic reionization history. The afterglows of GRBs generally have broken power-law spectra, so it is possible to extract intergalactic medium (IGM) absorption features. We also present the capability of high-redshift GRBs to probe the pre-galactic metal enrichment and the first stars. ; Comment: 21 pages, 24 figures, Accepted for publication by New Astronomy Reviews