  Let G be a non-elementary group of isometries of a proper CAT(0)-space with
limit set L. We survey properties of the action of G on L under the assumption
that G contains a rank-one element. Among others, we show that there is a dense
orbit for the action of G on the complement of the diagonal in LxL and that
pairs of fixed points of rank-one elements are dense in the complement of the
diagonal of LxL.
