Textiles have a very long history, but they are far from becoming outdated. They gain new importance in technical applications, and man-made fibers are at the center of this ongoing innovation. The development of high-tech textiles relies on enhancements of fiber raw materials and processing techniques. Today, melt spinning of polymers is the most commonly used method for manufacturing commercial fibers, due to the simplicity of the production line, high spinning velocities, low production cost and environmental friendliness. Topics covered in this review are established and novel polymers, additives and processes used in melt spinning. In addition, fundamental questions regarding fiber morphologies, structure-property relationships, as well as flow and draw instabilities are addressed. Multicomponent melt-spinning, where several functionalities can be combined in one fiber, is also discussed. Finally, textile applications and melt-spun fiber specialties are presented, which emphasize how ongoing research efforts keep the high value of fibers and textiles alive.