Muonium centers are readily formed in a wide variety of insulators and semiconductors due to enormous capture cross sections of the unscreened Coulomb potential produced by positive muons. Following the initial capture, different processes of electron localization produce two basically different muonium atoms—deep centers with the characteristic length scale of about the Bohr radius and shallow centers where electron is delocalized over many dozens of lattice spacings. In magnetic semiconductors, additional localization mechanism—exchange interaction–causes electron localization around the muon within about one lattice spacing. This novel muonium center—bound magnetic polaron—is found in Eu and Sm chalcogenides and ferromagnetic spinels.