The common physical basis of the Mossbauer effect (ME) and the nuclear magnetic resonance (NMR) methods is shortly reviewed by discussing the relevant physical properties of nuclei and the interactions of atomic nuclei with electric and magnetic fields. A survey is given of the measurement methods. In principle all those properties of materials can be measured by ME and NMR which influence the energy levels of atomic nuclei and change the shape and intensity of ME and NMR spectra. These properties include the magnetic hyperfine field present in magnetically ordered materials, the valency state of atoms influencing the charge density at the nucleus, the local symmetry of the neighborhood of an atom resulting in electric field gradients at the nucleus, etc. Macroscopic properties connected with these microscopic properties are the magnetization, the magnetic, electric and structural order of crystals, lattice imperfections, and size, shape, and texture of crystallites. Most of these physical properties are closely related to the magnetic properties of matter. Both ME and NMR are limited to specific isotopes and therefore only special groups of' materials are accessible for investigation by these methods. Extensive data about NMR investigations on these materials in the last five years and complementary information about ME investigations on these materials are presented in tabular form and are discussed for selected examples.