  The purpose of this paper is to both survey and offer some new results on the
non-triviality of the characteristic classes of Riemannian foliations. We give
examples where the primary Pontrjagin classes are all linearly independent. The
independence of the secondary classes is also discussed, along with their total
variation. Finally, we give a negative solution of a conjecture that the map of
classifying spaces $\FRGq \to \FGq$ is trivial for codimension $q > 1$.
