A review of the magnetism in the parent compounds of the iron-based superconductors is given based on the transmission Mossbauer spectroscopy of Fe-57 and Eu-151. It was found that the 3d magnetism is of the itinerant character with varying admixture of the spin-polarized covalent bonds. For the '122' compounds, a longitudinal spin density wave (SDW) develops. In the case of the EuFe2As2, a divalent europium arranges in an anti-ferromagnetical order at a much lower temperature as compared with the onset of SDW. These two magnetic systems remain almost uncoupled one to another. For the non-stoichiometric Fe1+xTe parent of the '11' family, one has a transversal SDW and magnetic order of the interstitial iron with relatively high and localized magnetic moments. These two systems are strongly coupled one to another. For the 'grand parent' of the iron-based superconductors FeAs, one observes two mutually orthogonal phase-related transversal SDW on the iron sites. There are two sets of such spin arrangements due to two crystallographic iron sites. The FeAs exhibits the highest covalency among the compounds studied, but it has still a metallic character.