A short review of the conventional methods of Mössbauer filtration (obtaining highly monochromatized radiation limited only by the energy width of the Mössbauer line) is presented and some new proposals related to the Mössbauer filtration of synchrotron radiation (SR) are discussed. Among the conventional methods of Mössbauer SR filtration there are pure nuclear reflections in Mössbauer diffraction of SR, so-called GIAR-films, total external reflection of SR from the surface of a sample enriched with the Mössbauer isotope, diffraction on artificially grown multilayers with the alternating concentration of the Mössbauer isotope. Each method has its own advantages and dis-advantages, so the search for further possibilities for SR Mössbauer filtration is of great importance. The main attention is paid to the new theoretical proposals on Mössbauer filtration of SR: the total internal reflection from the isotope interface (a plane interface dividing the sample into two regions with the different concentration of the Mössbauer isotope), the Mössbauer surface waveguide modes in media with periodic spatial modulation of the Mössbauer isotope concentration and inelastic coherent Mössbauer forward scattering of SR. For specific models of the phenomena mentioned, a theoretical analysis has been carried out by both an analytical approach and numerical calculations. It has been found that the spectral characteristics of filtered SR for the proposed approaches differ from those for the conventional methods. The prospects of the experimental realization of the proposed new methods of Mössbauer filtration have been discussed.