We study quantum matter driven far from equilibrium by strong external fields that push systems beyond conventional physical limits. In this regime, the interplay between coherent driving and many body interactions can generate complex behavior and give rise to emergent non equilibrium phases, including topological states, magnetism, and superconductivity. To understand and control these phenomena, we develop theoretical and computational approaches based on non equilibrium quantum field theory, Floquet engineering, and semiclassical dynamics.