  We study Sushchansky p-groups. We recall the original definition and
translate it into the language of automata groups. The original actions of
Sushchansky groups on p-ary tree are not level-transitive and we describe their
orbit trees. This allows us to simplify the definition and prove that these
groups admit faithful level-transitive actions on the same tree. Certain branch
structures in their self-similar closures are established. We provide the
connection with, so-called, G groups that shows that all Sushchansky groups
have intermediate growth and allows to obtain an upper bound on their period
growth functions.
