Combining experiments and numerical simulations with a mechanical-statistical model of twisted yarns, we discuss the spinning transition between a cohesionless assembly of fibers into a yarn. We show that this transition is continuous but very sharp due to a giant amplification of frictional forces which scales as expθ^{2}, where θ is the twist angle. We demonstrate that this transition is controlled solely by a nondimensional number H involving twist, friction coefficient, and geometric lengths. A critical value of this number H_{c}≃30 can be linked to a locking of the fibers together as the tensile strength is reached. This critical value imposes that yarns must be very slender structures with a given pitch. It also induces the existence of an optimal yarn radius. Predictions of our theory are successfully compared to yarns made from natural cotton fibers.