  In this survey, we gather together various results on the action of a real
form of a complex semisimple Lie group on its flag manifolds. We start with the
finiteness theorem of J.Wolf implying that at least one of the orbits is open.
We give a new proof of the converse statement for real forms of inner type,
essentially due to F.M.Malyshev. Namely, if a real semisimple Lie group of
inner type has an open orbit on an algebraic homogeneous space of the
complexified group then the homogeneous space is a flag manifold. To prove
this, we recall, partly with proofs, some results of A.L.Onishchik on the
factorizations of reductive groups. Finally, we discuss the cycle spaces of
open orbits and define the crown of a symmetric space of non-compact type. With
some exceptions, the cycle space agrees with the crown. We sketch a complex
analytic proof of this result, due to G.Fels, A.Huckleberry and J.Wolf.
