Gamma-ray bursts (GRBs) have puzzled astronomers since their accidental discovery in the late 1960s. The BATSE detector on the COMPTON-GRO satellite has been detecting one burst per day for the last six years. Its findings have revolutionized our ideas about the nature of these objects. They have shown that GRBs are at cosmological distances. This idea was accepted with difficulties at first. The recent discovery of an X-ray afterglow by the Italian/Dutch satellite BeppoSAX has led to a detection of high red-shift absorption lines in the optical afterglow of GRB970508 and in several other bursts and to the identification of host galaxies to others. This has confirmed the cosmological origin. Cosmological GRBs release ~1051-1053erg in a few seconds making them the most (electromagnetically) luminous objects in the Universe. The simplest, most conventional, and practically inevitable, interpretation of these observations is that GRBs result from the conversion of the kinetic energy of ultra-relativistic particles or possibly the electromagnetic energy of a Poynting flux to radiation in an optically thin region. This generic ``fireball'' model has also been confirmed by the afterglow observations. The ``inner engine'' that accelerates the relativistic flow is hidden from direct observations. Consequently, it is difficult to infer its structure directly from current observations. Recent studies show, however, that this ``inner engine'' is responsible for the complicated temporal structure observed in GRBs. This temporal structure and energy considerations indicates that the ``inner engine'' is associated with the formation of a compact object - most likely a black hole.