The thesis is devoted to magnetic metamaterials operating in the frequency range of 10 MHz 1 GHz. Mechanisms of tailoring the properties of metamaterials are developed and a number of linear and nonlinear applications is proposed.In Chapter 1, the introduction to the field of metamaterials is given and the main goal of the thesis is defined as the search for possible applications of low-frequency metamaterials. The main motivation is the potential of magnetic metamaterials in Magnetic Resonance Imaging (MRI).Chapter 2 briefly summarizes the near-field properties of magnetic metamaterials. Magnetic coupling between a pair of metamaterial elements is described and magnetoinductive (MI) waves propagating on the metamaterials arrays are introduced.In Chapter 3, the magnetic coupling between the elements is studied in more detail. Based on the analogy between MI waves and acoustic waves in solids, "diatomic" metamaterial arrays having two elements per unit cell are introduced. It is shown that by changing the resonant frequencies of the elements and the coupling between them it is possible to acquire additional freedom in tailoring the dispersion properties of MI waves compared to simple "monatomic" configurations.In Chapter 4, various linear applications of metamaterials are discussed. They are shift-dependent transmission, subwavelength imaging and focusing, and rotational resonance of MI waves. It is shown that the microscopic model based on taking the interaction between the elements into account allows for reliable explanation of the phenomena studied.In Chapter 5, a nonlinear application, parametric amplification of MI waves, is discussed. It is shown that parametric amplification can lead to the compensation of loss in metamaterials and to increase of the power extracted from an MRI detection system.Conclusions are drawn and possible directions for future work are determined in Chapter 6.