Cosmic γ-ray bursts are one of the great frontiers of astrophysics today. They are a playground of relativists and observers alike. They may teach us about the death of stars and the birth of black holes, the physics in extreme conditions, and help us probe star formation in the distant and obscured universe. In this review we summarise some of the remarkable progress in this field over the past few years. While the nature of the GRB progenitors is still unsettled, it now appears likely that at least some bursts originate in explosions of very massive stars, or at least occur in or near the regions of massive star formation. The physics of the burst afterglows is reasonably well understood, and has been tested and confirmed very well by the observations. Bursts are found to be beamed, but with a broad range of jet opening angles; the mean γ-ray energies after the beaming corrections are åisebox-0.5ex 10$^51$ erg. Bursts are associated with faint (<R> i̊sebox-0.5ex 25 mag) galaxies at cosmological redshifts, with <z> rs̊ebox-0.5ex 1. The host galaxies span a range of luminosities and morphologies, but appear to be broadly typical for the normal, actively star-forming galaxy populations at comparable redshifts and magnitudes. Some of the challenges for the future include: the nature of the short bursts and possibly other types of bursts and transients; use of GRBs to probe the obscured star formation in the universe, and possibly as probes of the very early universe; and their detection as sources of high-energy particles and gravitational waves.