Today's magnetic memory and logic devices operate at gigahertz switching speeds. To achieve the faster terahertz regime will require new technologies, and ultrafast all-optical magnetic switching using coherent spin manipulation is a leading contender. In this talk, I use theory and experiment to show how the quantum-mechanical, non-thermal manipulation of spins with femtosecond laser pulse sequences could meet this challenge. This is a new principle, analogous to processes in femto-chemistry, where photo-products of chemical and biochemical reactions can be influenced by creating suitable superpositions of molecular states. Femtosecond-laser-excited coherence between electronic states can switch magnetic order non-adiabatically, by abruptly changing the delicate balance between competing phases of correlated materials. The creation of magnetic correlations within femtoseconds, i.e. faster than the period of lattice oscillations, reveals a new temporal regime of magnetism and opens new directions for manipulating materials out-of-equilibrium using Terahertz, Mid-infrared, and X-ray pulses. At the same time, by disentangling the strongly-coupled components of complex order parameters in the time domain, we may facilitate a profound understanding of a broader class of phase transitions in complex quantum materials. Recent References: Nature 496, 69 (2013) and Nature Communications 5,3229 (2014)