I consider the time evolution of observables and reduced density matrices after a sudden quench of a Hamiltonian parameter in one dimensional systems. I discuss the issue of relaxation and show quite generally that if subsystems relax and can be described in terms of a statistical ensemble, dynamical correlations are described by the same ensemble as well. Then I consider quenches in the transverse field Ising chain, where many exact results have been recently obtained. I focus on the approach to the stationary state (which, in the specific case, is a generalized Gibbs ensemble) and discuss the relation between time averages and late time dynamics.