  We survey some recent progress in the study of algebraic varieties X with log
terminal singularities, especially, the uni-ruledness of the smooth locus X^0
of X, the fundamental group of X^0 and the automorphisms group on (smooth or
singular) X when dim X = 2. The full automorphism groups of a few interesting
types of K3 surfaces are described, mainly by Keum-Kondo.
  We conjecture that when X is Q-Fano then X^0 has a finite fundamental group,
which had been proved if either dim X < 3 or the Fano index is bigger than dim
X - 2. We also conjecture that when X is a log Enriques (e.g. a normal K3 or a
normal Enriques) surface then either pi_1(X^0) is finite or X has an abelian
surface as its quasi-etale cover, which has been proved by Catanese-Keum-Oguiso
under some extra conditions.
