  The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein-Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on nonrelativistic and special relativistic physics, {\it i.e.} to model
the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems.
In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
({\it i.e.} fluid models). This paper gives introductions to kinetic theory in
non-curved spacetimes and then the Einstein-Vlasov system is introduced. We
believe that a good understanding of kinetic theory in non-curved spacetimes is
fundamental to good comprehension of kinetic theory in general relativity.
