The problem of coexistence between charge-density-waves (CDWs) and superconductivity is revisited. Recent evidence was analyzed for different classes of materials with the emphasis on high-<$ET sub c> oxides. For the latter, the model of the d-wave or extended s-wave Cooper pairing competing with checkerboard or unidirectional CDWs is suggested. The corresponding phase diagrams were plotted and used as a guide to predict new features in the tunnel or photoemission spectra. In the framework of the model concerned, dc Josephson tunneling through junctions involving CDW superconductors is examined. It is shown that CDWs distort current dependences on the angle between crystal axes and the junction plane inherent to d-wave superconductors leading to an extra periodicity.