Quantum statistical physics and condensed matter traditionally deal with the collective behavior of systems in thermal equilibrium. Here remarkable emerging phenomena are known to occur at low energy, as a result of strong interactions and quantum statistics. An intriguing theoretical question, which has recently found several experimental motivations and is currently attracting enormous interest, is to what extent genuine quantum phenomena can survive far away from equilibrium. In this talk I will review the motivations and the main theoretical questions behind this research and discuss the recent progress in the general understanding of strongly interacting quantum systems far from equilibrium.