This review addresses the physical properties of the σ -phase in Fe-Cr and Fe-V alloy systems as revealed both with experimental-mostly with the Mössbauer spectroscopy-and theoretical methods. In particular, the following questions relevant to the issue have been addressed: identification of σ and determination of its structural properties, kinetics of α-to-σ and σ -to-α phase transformations, Debye temperature and Fe-partial phonon density of states, Curie temperature and magnetization, hyperfine fields, isomer shifts and electric field gradients.