  We review stability and instability results for self-gravitating matter
distributions, where the matter model is a collisionless gas as described by
the Vlasov equation. The focus is on the general relativistic situation, i.e.,
on steady states of the Einstein-Vlasov system and their stability properties.
In order to put things into perspective we include the Vlasov-Poisson system
and the relativistic Vlasov-Poisson system into the discussion.
