The results of theoretical and experimental investigations of V.V. Lednev on interactions of weak and extremely weak magnetic fields with biosystems have been reviewed. The period since 1989, when the first version of the interference model has been suggested, until now has been considered. Some mathematical expressions, are presented, which have been published earlier in the papers that are now bibliographic rarity. The results of experimental investigations are also summarized that have been performed in this period under the supervision of V.V. Lednev in the laboratory of biophysics of intracellular regulation in the Institute of Theoretical and Experimental Biophysics of the Russian Academy of Sciences.