The positron-electron bound system in condensed matter (Ps) is a probe of primary importance for the investigation of the microscopic structure of liquids and non-metallic solids. The physical properties of Ps in matter are generally different with respect to Psin vacuo, owing to the interactions with the surrounding electrons. Information on the structure of Ps can be obtained through the Zeeman effect, that induces a mixing of them=0 Ps ground state sublevels with a shortening of the triplet lifetime (magnetic quenching). This method, which can be coupled with any positron annihilation experimental technique, showed its effectiveness to discriminate among competitive reactions between Ps and the surrounding medium, as well as to clarify the origin of lifetime components of uncertain attribution. The discovery of anomalous magnetic effects in different organic liquids and solids has opened new perspectives in the studies of positron-multielectrons bound systems. Magnetic quenching experiments carried out with polarized positron beams display a complex and fascinating phenomenology, whose explanation could shed light on the role of the positron-medium interactions which take place within the early instants after the emission of the positron. In the present paper various aspects of the magnetic quenching method will be examined, with emphasis on recent experimental results.