Complex quantum systems out of equilibrium are not only at the basis of some of the most intriguing puzzles in physics, they also allow for new applications in quantum technologies. Equipped with a portfolio of innovative methods, this proposal makes a concerted and focused effort to tackle some of the difficult questions on strongly correlated systems out of equilibrium. At the same time it suggests new modes of quantum technologies by intrinsically exploiting notions of openness and non-equilibrium. The proposed work will be structured according to four methodologically intertwined objectives: 1. A fresh attempt will be made at solving long-standing questions of equilibration and thermalization of interacting quantum many-body systems. Precise conditions will be given under which thermalization provably does, or does not, happen. 2. It will be shown that notions of exactly timed, controlled and protected quantum information processing are possible not despite of, but because of quantum many-body systems undergoing non-equilibrium dynamics and dissipation. This research will employ innovative and highly unorthodox Markov chain mixing tools, applied to the quantum domain for the first time. 3. Based on new insights on the entanglement structure of systems in non-equilibrium, new algorithms will be proposed that promise to overcome the road block of numerically simulating long time dynamics being prohibitively difficult, and which are suitable for simulating the evolution of quantum fields. 4. Experimental progress in non-equilibrium dynamics will slow down dramatically unless new probing techniques are developed. New paths will be taken to achieve efficient dynamical system identification, based on novel paradigms of quantum compressed sensing. This high-risk, high-gain research promises truly ground breaking results on long-standing fundamental problems as well as on innovative applications in quantum technologies.