  In this short review article we sketch some developments which should
ultimately lead to the analogy of the Chern-Weil homomorphism for principal
bundles in the realm of non-commutative differential geometry. Principal
bundles there should have Hopf algebras as structure `cogroups'. Since the
usual machinery of Lie algebras, connection forms, etc\., just is not available
in this setting, we base our approach on the Fr\"olicher--Nijenhuis bracket.
