Great experimental advances over the last decades have made it possible to realize quantum systems of many interacting particles that are, to a good approximation, isolated from their environments, and allow for unprecedented control over various properties of such systems in terms. These novel quantum simulators probe quantum physics in unexplored regimes, thereby bringing to light fundamental theoretical questions and new practical applications. As these devices usually operate far from thermal equilibrium, most existing tools in a theoretical physicist's toolbox fail to capture their behavior and new analytical and numerical methods are required. The PhD applican's research will contribute to this effort, by developing new numerical and analytical techniques to study non-equilibrium quantum dynamics. Two of the main focuses of this research will be understanding the growth of quantum entanglement due to interactions and calculating transport properties. The latter also ties to important problems in traditional condensed matter physics.