  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 non-relativistic and special relativistic physics, 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.
