Meteorites are the space messengers bringing us the unique information about the Solar System formation and evolution as well as about the effects of various extreme space conditions on meteorites and their parent bodies. The main iron-bearing compounds in meteorites are Fe-Ni-Co alloy, olivine (Fe, Mg)2SiO4, orthopyroxene (Fe, Mg)SiO3, clinopyroxene (Ca, Fe, Mg)SiO3, troilite FeS, chromite FeCr2O4, hercynite FeAl2O4, ilmenite FeTiO3, daubréelite FeCr2S4, schreibersite (Fe, Ni)3P and some other compounds. Therefore, 57Fe Mössbauer spectroscopy was successfully applied for the analyses of various meteorites for about 60 years of experience. The development of Mössbauer spectrometers with a high velocity resolution, i.e., with a high discretization of the velocity reference signal up to 212, provides much better adjustment to resonance and significantly increases the spectra quality and analytical possibilities of Mössbauer spectroscopy. In fact, this permits us to decompose the complex Mössbauer spectra of meteorites using the larger number of spectral components related to reliable compounds in comparison with the results obtained using conventional Mössbauer spectrometers with discretization of the velocity reference signal up to 29. In the present review we consider the results and advances of various meteorites analyses by means of Mössbauer spectroscopy with a high velocity resolution.