$\theta$-groups as children's play

Theta-representations were introduced by Vinberg in the 70-s.
They arise from Z or Z/mZ gradings of simple Lie algebras g as the
actions of G_0 (connected group corresponding to the grading component
g_0) on g_1. theta-representations inherit Jordan decomposition from g
and together with it a lot of other nice properties. For example,
there are only finitely many nilpotent orbits and it is possible to
describe them, the algebra of polynomial G_0-invariants on g_1 is a
free algebra, the quotient map is equidimensional. There is an
analogue of the Weyl group and so on.
We will discuss various methods to deal with theta-group. In the case
of a classical g, everything basically boils down to Young diagrams
and in the exceptional case one is tempted to use the computer.