  The brief review and discussion of statement of some observational problems
of gamma-ray bursts (GRB), GRB host galaxies and star forming at small and
large redshifts: Are there similarities and differences between GRB hosts and
the typical galaxy population - this is currently the main question for the
study of GRB host galaxies. The direct connection between long-duration GRBs
and massive stars explosions, GRBs and some puzzles of core-collapse supernovae
are briefly discussed. On model-independent observational cosmological tests -
GRB rate and star forming rate at high redshifts.
