Invisible cloaking of material bodies using the wave flow method

The current knowledge of the physics of electromagnetic cloaking of material objects by the wave flow method is reviewed. Experiments demonstrating the feasibility of this cloaking method are described. Some aspects of calculating cloak profiles are examined, and achievements and unsolved problems in the theory of the interaction of electromagnetic waves with shells are considered. Prospects for developing the cloaking method for waves of other physical nature (acoustic and probability density waves) are discussed.