Recent experiments with ultra-cold atomic gases and trapped ions as well as solid-state devices such as superconducting circuits designed to manipulate q-bits, are posing a new challenge for theory. As in traditional atomic physics these systems are often prepared far from equilibrium, or continuously driven by electromagnetic fields. At the same time they retain a many-body character and intricate quantum correlations, which define a new class of quantum matter. I will first review recent experimental advances in this field and then address a theoretical question: Can the complexity of quantum dynamics in these systems give rise to robust universal phenomena in spite of the non-equilibrium conditions?