  We provide a comprehensive review of major developments in our understanding
of gamma-ray bursts, with particular focus on the discoveries made within the
last fifteen years when their true nature was uncovered. We describe the
observational properties of photons from the radio to multi-GeV bands, both in
the prompt emission and the afterglow phases. Mechanisms for the generation of
these photons in GRBs are discussed and confronted with observations to shed
light on the physical properties of these explosions, their progenitor stars
and the surrounding medium. After presenting observational evidence that a
powerful, collimated, jet moving at close to the speed of light is produced in
these explosions, we describe our current understanding regarding the
generation, acceleration, and dissipation of the jet and compare these
properties with jets associated with AGNs and pulsars. We discuss mounting
observational evidence that long duration GRBs are produced when massive stars
die, and that at least some short duration bursts are associated with old,
roughly solar mass, compact stars. The question of whether a black-hole or a
strongly magnetized, rapidly rotating neutron star is produced in these
explosions is also discussed. We provide a brief summary of what we have
learned about relativistic collisionless shocks and particle acceleration from
GRB afterglow studies, and discuss the current understanding of radiation
mechanism during the prompt emission phase. We discuss theoretical predictions
of possible high-energy neutrino emission from GRBs and the current
observational constraints. Finally, we discuss how these explosions may be used
to study cosmology, e.g. star formation, metal enrichment, reionization
history, as well as the formation of first stars and galaxies in the universe.
