This review discusses a number of questions related to the use of the muon method for the study of metals. The possibilities of the method for the study of normal metals, superconductors, and ferromagnetic materials are analyzed. A systematic comparison of theory and experiment is made. It is shown that the method permits determination of the local magnetic fields at crystallographic sites, the type of magnetic structure in complicated ferromagnetic crystals (rare earth metals), analysis of the magnetic texture (grain orientation) of electrical steels, diagnosis of the interstitial sites occupied by a proton or muon, determination of the diffusion rate and the degree of distortion of the crystal lattice, and study of phase transitions in rare earth metals and spin glasses. In normal metals the muon method permits determination both of the muon diffusion rate and of the nature of diffusion (classical or quantum), the Knight shift in the muon, the charge state of a proton or muon in the metal, and the distortion of the crystal lattice. For superconductors the method permits information to be obtained which is inaccessible by other means, particularly determination of the ratio of the normal and superconducting phases and study of the dynamics of destruction and appearance of the superconducting state. The prospects for development of the muon method for study of the properties of metals are demonstrated.