During the last decade considerable efforts have been made in the sciences and technology for controlling or engineering the magnetic properties of various materials. For example, a number of artificially arranged materials were engineered to facilitate electromagnetic, acoustic, spin and plasmonic waves propagation in particular directions or in specific regions only. Such materials also enable to be localized in chosen channels or zones, or even prohibit the propagation of these waves completely. They are now known as photonic, phononic, plasmonic and magnonic crystals. In my report I review a number of physical effects related to investigations of these crystals which we discovered and extensively studied during conduction of the current Project. Among them are various linear and nonlinear effects: solitons, dissipative solitons, gap solitons, defect modes, nonresiprocity waves, edge waves etc. I report also a considerable progress in application of our results in electronic industry. In particular, RFID tags based on surface acoustic waves operating at 6 GHz for the first time in the world were developed in our lab and currently are being adopted by industry.