In contrast to equilibrium quantum systems, which exist in just a tiny corner of an immense configuration space, non-equilibrium quantum many-body systems can access the totality of configuration space and represent a rich resource for novel quantum states, including light-induced quantum-coherent phases of matter, topological phases and spin textures in solids and cold atom systems. Non-equilibrium many-body quantum dynamics is perhaps the last frontier in physics, where even the basic understanding is still lacking and a number of outstanding fundamental questions are wide open. However, there has been much recent progress in exploring these fundamental aspects on both theoretical and experimental sides.