The proximity effect in superconductor-ferromagnet (S/F) heterostructures is characterized by the damped oscillatory behavior of the Cooper pair wave function in the ferromagnet. This phenomenon is analogous to the inhomogeneous superconductivity predicted by Larkin and Ovchinnikov (1964) and Fulde and Ferrell (1964). The author provides a unified description of the properties of S/F heterostructures, emphasizing the non-monotonous dependence of the critical temperature of multilayers and bilayers on the ferromagnetic layer thickness and the realization of π⁻ Josephson junctions. Recent experimental progress has enabled the observation of various effects in high-quality S/F systems, including domain-wall superconductivity and the influence of superconductivity on magnetic structures. The paper discusses the domain-wall superconductivity in S/F bilayers and the inverse influence of superconductivity on ferromagnetism, which favors non-uniform magnetic structures. It also highlights the importance of the proximity effect in studying superconducting electrons under a strong exchange field and the interplay between superconductivity and magnetism in controlled systems. The paper reviews the theoretical and experimental developments in S/F heterostructures, including the generalized Ginzburg-Landau functional, the proximity effect in ferromagnets, and the oscillatory behavior of the superconducting transition temperature in S/F multilayers and bilayers. The study also covers the spin-valve effect in complex S/F structures and the potential applications of these systems. The paper concludes with a discussion of the implications of the proximity effect in S/F systems and the need for further research in this area.The proximity effect in superconductor-ferromagnet (S/F) heterostructures is characterized by the damped oscillatory behavior of the Cooper pair wave function in the ferromagnet. This phenomenon is analogous to the inhomogeneous superconductivity predicted by Larkin and Ovchinnikov (1964) and Fulde and Ferrell (1964). The author provides a unified description of the properties of S/F heterostructures, emphasizing the non-monotonous dependence of the critical temperature of multilayers and bilayers on the ferromagnetic layer thickness and the realization of π⁻ Josephson junctions. Recent experimental progress has enabled the observation of various effects in high-quality S/F systems, including domain-wall superconductivity and the influence of superconductivity on magnetic structures. The paper discusses the domain-wall superconductivity in S/F bilayers and the inverse influence of superconductivity on ferromagnetism, which favors non-uniform magnetic structures. It also highlights the importance of the proximity effect in studying superconducting electrons under a strong exchange field and the interplay between superconductivity and magnetism in controlled systems. The paper reviews the theoretical and experimental developments in S/F heterostructures, including the generalized Ginzburg-Landau functional, the proximity effect in ferromagnets, and the oscillatory behavior of the superconducting transition temperature in S/F multilayers and bilayers. The study also covers the spin-valve effect in complex S/F structures and the potential applications of these systems. The paper concludes with a discussion of the implications of the proximity effect in S/F systems and the need for further research in this area.