Understanding the quantum dynamics  of a complex quantum many­-body system is one of the biggest challenges in the field of quantum science. Most previous research has focused on the properties of ground or low temperature states in quantum many­ body systems. Due to the strong entanglement growth typically observed in the dynamics of quantum states far from equilibrium, understanding such a dynamics has remained a highly challenging and complex goal for theory. Controllable experiments ranging from collective atom-photon interactions in optical cavities and ensembles of strongly interacting atoms to quantum dynamics in optical lattices and  ensembles  of  atom-like  impurities  in  solid  state enable one to test and observe such complex quantum dynamics using completely new tools in experiment  and theory. This  includes the realization of a whole class of new quantum  phases of matter such as many-body localized states. In such systems, e.g. quantum phenomena persist even at very  high energies in the system  and a whole  class of new  phase transitions  can be observed and investigated. The combination of novel experimental tools and theoretical techniques promises a much deeper understanding in this field.  While still  in its infancy,  it is highly relevant to a broad class of questions ranging from how  temperature,  for  example, emerges in isolated quantum systems to the non-equilibrium evolution of the universe in cosmology.