The article covers developments in the representation theory of finite group
schemes over the last fifteen years. We start with the finite generation of
cohomology of a finite group scheme and proceed to discuss various consequences
and theories that ultimately grew out of that result. This includes the theory
of one-parameter subgroups and rank varieties for infinitesimal group schemes;
the π-points and Π-support spaces for finite group schemes, modules of
constant rank and constant Jordan type, and construction of bundles on
projective varieties associated with cohomology ring of an infinitesimal group
scheme G. In the last section we discuss varieties of elementary subalgebras
of modular Lie algebras, generalizations of modules of constant Jordan type,
and new constructions of bundles on projective varieties associated to a
modular Lie algebra.Comment: 31 pag