Non-equilibrium quantum systems represent one of the most promising
possibilities for realizing novel states of matter. I will consider the non
equilibrium situation known as quantum quench, in which a closed system
evolves from an initial state that is not a Hamiltonian eigenstate such as those
achieved by suddenly switching a control parameter. An important question is
under what conditions the system reaches a stationary state and in which
circumstances this state is characterized by an effective "thermal", i.e.
equilibrium, distribution. I will discuss how to obtain the time evolution of
observables and correlation functions with a variety of theoretical techniques
including quantum field theory (in particular CFT) and integrability. These
approaches allow to have a rather complete understanding of the relaxation
dynamics and the most challenging open problems will be presented.