The melt-spinning technique offers an opportunity for tailoring magnetic properties by controlling the structures and microstructures in both single-phase and composite magnets. This review first broadly discusses the principle of cooling control, amorphization, crystallization, annealing, and consolidation of the melt-spun ribbons. The phase, microstructure, and magnetic properties of popular single-phase nanocrystalline magnets are reviewed, followed by the nanocomposite magnets consisting of magnetically hard and soft phases. The precipitation-hardened magnetic materials prepared by melt spinning are also discussed. Finally, the role of intergrain exchange coupling, thermal fluctuation, and reversible/irreversible magnetization processes are discussed and correlated to the magnetic phenomena in both single-phase and nanocomposite magnets.