The positions of over 1000 gamma-ray bursts detected with the BATSE ex
periment on board the Compton Gamma Ray Observatory are uniformly and
randomly distributed in the sky, with no significant concentration to
the galactic plane or to the galactic center. The strong gamma-ray bur
sts have an intensity distribution consistent with a number density in
dependent of distance in Euclidean space. Weak gamma-ray bursts are re
latively rare, indicating that either their number density is reduced
at large distances or that the space in which they are distributed is
non-Euclidean. In other words, we appear to be at the center of a sphe
rical and bounded distribution of bursters. This is consistent with th
e distribution of all objects that are known to be at cosmological dis
tances (Like galaxies and quasars), but inconsistent with the distribu
tion of any objects which are known to be in our galaxy (like stars an
d globular clusters). If the bursters are at cosmological distances th
en the weakest bursts should be redshifted, i.e., on average their dur
ations should be longer and their spectra should be softer than the co
rresponding quantities for the strong bursts. There is some evidence f
or both effects in the BATSE data. At this time the cosmological dista
nce scale is strongly favored over the galactic one, but is not proven
. A definite proof (or disproof) could be provided with the results of
a search for very weak bursts in the Andromeda galaxy (M31) with an i
nstrument similar to 10 times more sensitive than BATSE. If the burste
rs are indeed at cosmological distances then they are the most luminou
s sources of electromagnetic radiation known in the Universe. At this
time we have no clue as to their nature, even though well over a hundr
ed suggestions have been published in the scientific journals. An expe
riment providing similar to 1 arcsecond positions would greatly improv
e the likelihood that counterparts of gamma-ray bursters are finally f
ound. A new interplanetary network would offer the best opportunity.