  A brief exposition of the general theory of characteristic classes of quantum
principal bundles is given. The theory of quantum characteristic classes
incorporates ideas of classical Weil theory into the conceptual framework of
non-commutative differential geometry. A purely cohomological interpretation of
the Weil homomorphism is given, together with a standard geometrical
interpretation via quantum invariant polynomials. A natural spectral sequence
is described. Some quantum phenomena appearing in the formalism are discussed.
