  We discuss some new results concerning Gap Conjecture on group growth and
present a reduction of it (and its *-version) to several special classes of
groups. Namely we show that its validity for the classes of simple groups and
residually finite groups will imply the Gap Conjecture in full generality. A
similar type reduction holds if the Conjecture is valid for residually
polycyclic groups and just-infinite groups. The cases of residually solvable
groups and right orderable groups are considered as well.
