The technological demand to bump the Gigahertz switching speed limit of today's magnetic memory and logic devices into the Terahertz regime underlies the entire field of spin-electronics and integrated multi-functional nano-devices. In this talk, I use theory and experiment to show how all-optical switching based on the quantum-mechanical manipulation of spins and magnetic order with a train of phase-coherent laser pulses, by tuning phase and color, could meet this challenge. The creation of magnetic correlations within femtoseconds, i.e. faster than one period of lattice oscillations, reveals a new temporal regime of quantum-femtosecond magnetism. This field opens new directions for manipulating materials out-of-equilibrium with bursts of light, using Terahertz, Mid-infrared, and X-ray pulses.