Cremona groups and birational rigidity

The Cremona group Cr(n) in n variables is the group of
birational selfmaps of
the projective space P^n.
The classification of finite subgroups of Cr(n) is a classical problem which
is completed now only in dimension n=2.
We discuss higher-dimensional generalizations and relations between this
problem
and  the notion of equivariant birational rigidity.