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A deep and abiding mystery is one of the greatest treasures nature has to offer to scientists and the public alike. Gamma-ray bursts have been observed for over 20 years. More than 2000 papers have been published about them and numerous theoretical models proposed, yet no one knows for sure what they are, where they come from, or even if they are a single class of phenomena. Isotropy and confinement (i.e., a deficiency of faint sources compared to that expected for an unbounded homogeneous sample), as exhibited in the BATSE observations from the Compton Gamma-Ray Observatory, have lead us to consider seriously only two sites - an extended Galactic halo populated by neutron stars, or else cosmologically distant sources. Models of both varieties will be reviewed. At the present time, both classes of models are given about equal credence, though ALL current models make troublesome assumptions requiring clarification. Halo models have received several boosts lately, including the realization that the mean velocity of pulsars is greater than previously thought, the certain localization of two out of three (and possibly all) soft gamma-ray repeaters to supernova remnants in our Galaxy and in the LMC, and calculations to show that under certain, albeit highly restrictive assumptions, the BATSE statistics can be satisfied by high velocity neutron stars ejected from the Galaxy. Several current halo oriented theories would like to relate the soft repeaters to the more common ``classical" bursts and claim that the former are an earlier evolutionary stage of the latter. If, on the other hand, the soft repeaters are a separate class, as the cosmologists would require, perhaps there are other classes as well. Amid all this theoretical speculation, the solution to the gamma-ray burst riddle will most likely come from further observation. Some prospects for future observations, especially with the High Energy Transient Experiment, will be briefly discussed.
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