The thermodynamic and ab initio molecular-dynamics approaches are applied to analyse the phase transitions in the Fe—Zr system. First-principles molecular-dynamics simulations of the amorphization and crystallization processes in the Fe—Zr system are presented. The atomic positions in the Fe$_{29}$Zr$_{3}$ supercell are modelled by simulating annealing with usage of the density functional theory in the generalized gradient approximation. Changes in the electron density of states for the Fe$_{29}$Zr$_{3}$ supercell under liquid—amorphous—crystalline phase transitions are discussed. The most marked difference between the electronic spectra of the liquid and amorphous phases is a pseudogap at the Fermi level that is consistent with the Nagel—Tauc electronic criterion of the amorphous metallic-alloy thermal stability. Further simulating annealing in the isothermal/isenthalpic ensemble under the higher temperatures leads to the drastically changes of the electronic spectrum and rearrangement of atoms, which we assign to the first stage of the amorphous-alloy crystallization. The concentration dependence of relative integral Gibbs’ free energy for the initial amorphous $\alpha$-phase are constructed; this dependence has a specific S-shaped appearance (due to both the great value of relative volume change during the formation of the alloy and the negative value of entropy) that indicates a tendency of alloys to phase separation. The thermodynamic method confirms that the processes of phase formation in binary alloys of Fe—Zr system pass in two stages: at first, the processes of phase separation into two amorphous phases by means of the spinodal mechanism are observed; then, each phase of amorphous ones resulting from separation begins to crystallise. The concentration area of amorphization of Fe—Zr system alloys is calculated; the results are in a good agreement with experimental data.