Binary iron–nickel alloys are a convenient model system, on which the martensitic $\gamma \leftrightarrow \alpha$ transformation in iron alloys is studied for a considerable period of time. At the same time, these alloys are classical invars and are widely studied in connection with the ‘invar problem’. Until recently, the ‘features of the martensitic transformation in iron alloys’ and the ‘invar problem’ are considered separately. Taking into account the influence of the austenite magnetic state on the martensitic transformation leads to the discovery of another mechanism—‘magnetic $\gamma \rightarrow \alpha$ transition’. The aim of this work is to find the centres of martensitic transformation in these materials. As assumed, there are three types of martensitic points for steels and iron alloys, each of which has its own characteristic physical content and leads to one of the following transitions: ‘isothermal’, ‘ordinary athermal’ and ‘magnetic athermal’. The first two $\gamma \leftrightarrow \alpha$ transitions are realized at dislocation embryos, which are formed of crystal-structure defects existing in austenite. The magnetic transition occurs on magnetic concentration inhomogeneities with a disoriented magnetic structure formed because of competition between iron (antiferromagnetism) and nickel (ferromagnetism) atoms. Forced magnetostriction during the paraprocess and spontaneous magnetostriction below the Curie point lead to an increase in the interatomic distance and the appearance of collinear ferromagnetism in these inhomogeneities with a change in the co-ordination number from 12 to 8. Strong comprehensive pressure reduces the interatomic distance and leads to the formation of collinear antiferromagnetism within them and $\gamma$-phase stabilization. The current understanding of the critical sizes of dislocation embryos, above which their avalanche-like growth is observed, and the sizes of magnetic inhomogeneities (by volume) in the Fe–Ni system indicate values of the same order. The experimental criterion for the magnetic $\gamma \rightarrow \alpha$ transition in steels and alloys based on the Fe–Ni-invar is an abnormally large value of the martensitic point displacement in a strong magnetic field: $\Delta M_{s}/\Delta H \geqslant$ 3 K/(MA/m).