The results of theoretical and experimental investigations of the spectra of and the kinetic phenomena occurring in materials with magnetic-impurity states on impurities with a finite-range potential are reviewed. The spectra of magnetic-impurity states for different types of negative ions in strong magnetic fields are studied: weakly bound electron with an isotropic effective mass, negative ion with a markedly anisotropic electronic energy spectrum, and the H$^-$ system. The current status of the theory of transverse galvanomagnetic phenomena, stemming from the interaction of carriers with neutral impurities having a potential with a finite range, is discussed. Current theoretical and experimental results concerning oscillation effects in quantizing magnetic fields on different types of negative ions in semimetals and semiconductors are compared.