  A brief review is presented on the studies of the hole motion in a
two--dimensional quantum antiferromagnet. An extended introduction is given to
cover the background of the problem. The quantum Bogoliubov--de Gennes
formalism which treats the local distortion of the spin configuration and the
quantum renormalization process on an equal footing, is outlined. The latest
development on the central issue, whether a hole can freely propagate on an
antiferromagnetic background, is overviewed.
