The literature (experimental and theoretical) data on the tetragonality of martensite with interstitial–substitutional alloying elements and vacancies are reviewed and analysed. Special attention is paid to the studying the martensitic αʺ-Fe16N2-type phase with unique and promising magnetic properties as an alternative to the rare-earth intermetallics or permendur on the world market of the production of permanent magnets. The period since its discovery to the current status of research is covered. A statistical-thermodynamic model of ‘hybrid’ interstitial–substitutional solid solution based on a b.c.t. crystal lattice, where the alloying non-metal constituents (impurity atoms) can occupy both interstices and vacant sites of the host b.c.c.(t.)-lattice, is elaborated. The discrete (atomic-crystalline) lattice structure, the anisotropy of elasticity, and the ‘blocking’ and strain-induced (including ‘size’) effects in the interatomic interactions are taken into account. The model is adapted for the non-stoichiometric phase of Fe–N martensite maximally ordered by analogy with αʺ-Fe16N2, where nitrogen atoms are in the interstices and at the sites of b.c.t. iron above the Curie point. It is stressed an importance of adequate data on the available (in the literature) temperature- and concentration-dependent microscopic energy parameters of the interactions of atoms and vacancies. The features of varying (viz. non-monotonic decreasing with increasing temperature) the relative concentration of N atoms in the octahedral interstices of b.c.t. Fe, and therefore, the degree of its tetragonality (correlating with this concentration) are elucidated. Within the wide range of varying the total content of introduced N atoms, the ratio of the equilibrium concentration of residual site vacancies to the concentration of thermally activated vacancies in a pure b.c.c. Fe is demonstrated at a fixed temperature.