This paper presents a review of works related to the problem of development of soft-magnetic film Fe-based alloys exhibiting the combination of properties, such as the high saturation inductance, high level of soft-magnetic parameters over a wide range of MHz-frequencies, high wear-resistance and thermal stability, and an ability to be prepared by thin-film technologies. Magnetic cores of high-density recording heads are the principal application of these materials. Physical fundamentals of explanation of ferromagnetic behavior of a material with nano-sized structure, which have been developed for FINEMETs (Fe-Nb-Cu-Si-B) with the mixed amorphous + nanocrystalline structure, are considered. A new class of alloys Fe-Me-X (Me = Metal of III-V groups of the Periodic Table and X = C, N, O, and B) whose properties are higher that those of FINEMETs are discussed. The structure of these alloys consists of two nanocrystalline phases, such as the ferromagnetic a-Fe-based and nonmagnetic MeX phases. This structure provides the dispersion strengthening of the alloys. Metal science approaches to the selection of both chemical compositions and conditions of structure formation for these film alloys have been developed by authors and are discussed in this article.