Crystal structures of Fe–Ni alloys in extreme conditions (particularly, such as a state of the Earth’s interior core) at high pressure, $p$, and temperature, $T$, are reviewed. A role of magnetic effects in atomic ordering, interplay between the atomic and magnetic orders, and pressure effects on magnetic properties of Fe–Ni alloys (Curie temperature, $T_{C}$, ferromagnetic–antiferromagnetic phase transition, Invar effect) are analysed. Statistical-thermodynamic model of f.c.c. substitutional alloys with both magnetic components (within the framework of which, energy parameters of their exchange interactions and ‘interchange’ energy are determined) as well as models of kinetics of a relaxation of both shortrange and long-range atomic orders of Permalloy at zero pressure are considered with use of the self-consistent field approximation. External pressure is taken into account in statistical-thermodynamic and kinetic models of $L1_{2}$- or $D0_{19}$-type orderings for two cases, namely when dependences of volume of a sample of an alloy, $V$, on the long-range order parameter, $\eta$, and composition are weak or essential, i.e. when it is possible or it is impossible to neglect them, respectively. If this $V$ weakly depends on $\eta$ and composition, pressure does not influence $\Delta\eta|_{T_{K}}$-jump of the long-range order parameter. Pressure only displaces a point of the order–disorder phase transformation, $T_{K}$, aside high or low values of $T$, depending on signs of those parameters, which characterize model. The $T_{K}(p)$ and $\eta(p)$ dependences can be nonmonotonic, i.e. occurrence of two different points of order–disorder phase transformations appears possibly. If $V$ essentially depends on $\eta$ and composition, $\Delta\eta|_{T_{K}}$ is not a constant and can increase or decrease with increase of $p$. Dependence $T_{K}(p)$ is almost linear or nonlinear at low or high values of $p$, respectively. Pressure can promote atomic ordering or suppress it, change a kind of phase transition and symmetry of a crystal lattice of an alloy because of its transformation from tetragonal structure into rhombohedral one. The experimental data concerning characteristics of a (micro)heterogeneous structure of Fe–Ni Invar are discussed, and possible theoretical approaches for an explanation of their discrepancy are elucidated.