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.