  Riemannian and pseudo-Riemannian symmetric spaces with semisimple
transvection group are known and classified for a long time. Contrary to that
the description of pseudo-Riemannian symmetric spaces with non-semisimple
transvection group is an open problem. In the last years some progress on this
problem was achieved. In this survey article we want to explain these results
and some of their applications. Among other things, the material developed in
our previous papers math.DG/0312243, math.DG/0408249, and math.DG/0503220 is
presented in a unified way.
