Magnetotelluric and Magnetovariational Response Functions -- The Magnetotelluric Response Functions -- The Impedance Eigenstate Problem -- Separation of the Local and Regional Magnetotelluric Effects -- The Magnetovariational Response Functions -- The Recent Developments -- Basic Models of the Distortion Theory -- Two Classic Models of the Distortion Theory -- Models of the Near-Surface Distortions -- Models of Deep Geoelectric Structures -- Models of Deep Faults -- Interpretation of Magnetotelluric and Magnetovariational Data -- Statement of Inverse Problem -- The Interpretation Model -- Inversion Strategy. Magnetotelluric methods are finding increasing applications for imaging electrically conductive structures below the Earth`s surface in both industrial and academic research. In Models and Methods of Magnetotellurics, the authors provide a systematic approach to understanding the modern theory of ill-posed problems which is essential to making confident meaningful interpretation of magnetotelluric and magnetovariational soundings. The interpretation is conducted out in an interactive way, including the hypotheses tests and successive partial inversions with priority of the tippers, magnetic tensors and impedance-phases, which keeps out the destructive static effects of near-surface inhomogeneities. The efficiency of the interpretation is exemplified by new geoelectric models of the Baikal rift zone and the Cascadian subduction zone.