Recently nonequilibrium dynamics in synthetic quantum many-body systems (cold atoms in optical lattices, ion traps, Rydberg atoms) has been one of the most active frontiers in research in statistical and condensed matter physics. Nonequilibrium steady states, non-thermal behaviour, the propagation of excitations in the system as well as the presence of genuine dynamical phase transitions are only a few of the many issues that are presently under investigation. In this talk I will overview  the most intriguing questions and challenges in the field.