  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 $\pi$-points and $\Pi$-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.
