  Studies of the cosmic gamma-ray bursts (GRBs) and their host galaxies are now
starting to provide interesting or even unique new insights in observational
cosmology. Observed GRB host galaxies have a median magnitude R ~ 25 mag, and
show a range of luminosities, morphologies, and star formation rates, with a
median redshift z ~ 1. They represent a new way of identifying a population of
star-forming galaxies at cosmological redshifts, which is mostly independent of
the traditional selection methods. They seem to be broadly similar to the
normal field galaxy populations at comparable redshifts and magnitudes, and
indicate at most a mild luminosity evolution over the redshift range they
probe. Studies of GRB optical afterglows seen in absorption provide a powerful
new probe of the ISM in dense, central regions of their host galaxies, which is
complementary to the traditional studies using QSO absorption line systems.
Some GRB hosts are heavily obscured, and provide a new way to select a
population of cosmological sub-mm sources. A census of detected optical
tranistents may provide an important new way to constrain the total obscured
fraction of star formation over the history of the universe. Finally, detection
of GRB afterglows at high redshifts (z > 6) may provide a unique way to probe
the primordial star formation, massive IMF, early IGM, and chemical enrichment
at the end of the cosmic reionization era.
