The unrivalled, extreme luminosities of gamma-ray bursts (GRBs) make them the favored beacons for sampling the high redshift Universe. To employ GRBs to study the cosmic terrain -- e.g., star and galaxy formation history -- GRB luminosities must be calibrated, and the luminosity function versus redshift must be measured or inferred. Several nascent relationships between gamma-ray temporal or spectral indicators and luminosity or total energy have been reported. These measures promise to further our understanding of GRBs once the connections between the luminosity indicators and GRB jets and emission mechanisms are better elucidated. The current distribution of 33 redshifts determined from host galaxies and afterglows peaks near z ~ 1, whereas for the full BATSE sample of long bursts, the lag-luminosity relation predicts a broad peak z ~ 1-4 with a tail to z ~ 20, in rough agreement with theoretical models based on star formation considerations. For some GRB subclasses and apparently related phenomena -- short bursts, long-lag bursts, and X-ray flashes -- the present information on their redshift distributions is sparse or entirely lacking, and progress is expected in Swift era when prompt alerts become numerous.
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