Methods of description of ion–acoustic shock waves in dusty plasma are presented. A new type of dust ion–acoustic shock waves related to anomalous dissipation is described. The main dissipative processes related to charging of dust particles, absorption of ions by dust particles, Coulomb collisions between ions and dust particles, and Landau damping are analyzed. Proposed methods of theoretical analysis enable explaining all major specific features of dust ion–acoustic shock waves observed in the laboratory experiments. The shock waves of this type are present in the near-Earth plasma and the universe. Their investigation is possible in active ionospheric experiments of the Fluxus type. Important astrophysical problems in which the appearance of shock waves under consideration should be taken into consideration are the shock waves of supernovas, evolution of Local Interstellar medium, etc.