Starting from the notions of differential calculi, connections, curvatures, etc., on quantum principal bundles, one can proceed to defining characteristic classes for such bundles via a variant of the Chern-Weil map. In the talk, a variant of such a map, taking values in Hochschild homology of the base will be presented. We shall also discuss the possible ways to modify this construction to obtain cyclic-homology-valued characteristic classes.