Systems composed of several individual particles, called many-body systems, are at the heart of physics and in many ways even of science in general. Since Kepler first investigated the classical three-body problem, the search for universal descriptions of many-body systems has stimulated and fascinated generations of physicists and natural scientists alike. With the development of quantum theory and the concept of indistinguishable particles, the question of a full description of quantum many-body systems arose and was soon identified to be a very fundamental and complex problem. It is known that the correlations arising from strong interactions between particles in a many-body system very often completely dominate the system’s behaviour and lead to some of the most striking phenomena observed in nature, with high-temperature superconductivity and unconventional magnetism being two prominent examples. In the last decades substantial progress has been achieved in understanding the ground state properties of correlated many-body quantum systems, although some fundamental questions are still unsolved here. In contrast, very little is known on the dynamics of quantum systems far from equilibrium and on how correlations influence these dynamics.