A new class of phenomena discussed in this review is based on interaction between spatially separated, but closely located ferromagnets and superconductors. They are called Ferromagnet-Superconductor Hybrids (FSH). These systems include coupled smooth and textured Ferromagnetic and Superconducting films, magnetic dots, wires etc. The interaction may be provided by the magnetic flux from magnetic textures and supercurrents. The magnetic flux from magnetic textures or topological defects can pin vortices or create them, changing drastically the properties of the superconductor. On the other hand, the magnetic field from supercurrents (vortices) strongly interacts with the magnetic subsystem leading to formation of coupled magnetic-superconducting topological defects. We discuss possible experimental realization of the FSH. The presence of ferromagnetic layer can change dramatically the properties of the superconducting film due to proximity effect. We discuss experimental and theoretical studies of the proximity effect in the FSH including transition temperature, order parameter oscillations and triplet superconductivity.