[en] A review of the conventional ways of Moessbauer filtration is presented and some new proposals related to the M-filtration of synchrotron radiation (SR) are discussed. Among the traditional ways of Moessbauer SR filtration are pure nuclear reflections in Moessbauer diffraction of SR: total external reflection of SR at the surface of a sample containing Moessbauer isotope, diffraction at artificially grown multilayers with alternating concentration of the Moessbauer isotope. The main attention in the presentation is paid to the new theoretical proposals of Moessbauer filtration of SR. They are the total internal reflection at the isotope interface, the Moessbauer surface guided waves in media with a periodic space modulation of Moessbauer isotope concentration and inelastic coherent Moessbauer forward scattering of SR. It is found that the spectral characteristics of the filtrated SR differs from those ones for the convectional methods. The perspectives of experimental realization of the proposed new methods of the SR Moessbauer filtration are discussed