  The study of short-duration gamma-ray bursts (GRBs) has undergone a
revolution in recent years thanks to the discovery of the first afterglows and
host galaxies in May 2005. In this review we summarize our current knowledge of
the galactic and sub-galactic environments of short GRBs, and the implications
for the progenitor population. The most crucial results are: (i) some short
GRBs occur in elliptical galaxies; (ii) the majority of short GRBs occur in
star forming galaxies; (iii) the star forming hosts of short GRBs are distinct
from the host galaxies of long GRBs in terms of star formation rates,
luminosities, and metallicities, and instead appear to be drawn from the
general field galaxy population; (iv) the physical offsets of short GRBs
relative to their host galaxy centers are significantly larger than for long
GRBs; (v) the observed offset distribution agrees well with predictions for the
locations of NS-NS binary mergers; and (vi) unlike long GRBs, which tend to
occur in the brightest regions of their hosts, the environments of short GRBs
generally under-represent the light distribution of their host galaxies. Taken
together, these observations suggest that short GRB progenitors have a wide age
distribution and generally track stellar mass rather than star formation
activity. These results are fully consistent with NS-NS binary mergers, but
partial contribution from prompt or delayed magnetar formation is also
consistent with the data.
