As an important example, the existence of higher conservation laws prevents the onset of thermalisation, allowing for the emergence, at large times, of peculiar, non-thermal stationary states from the unitary many-body dynamics. These states can be described by a Generalized Gibbs Ensemble, a statistical ensemble which is reminiscent of the familiar Gibbs density matrix, but which takes into account also higher conserved operators. While this conceptual framework is now commonly accepted, obtaining quantitative predictions in many physically interesting situations is still extremely hard. The past few years have witnessed significant progress on this problem, based on the development of new analytical techniques rooted in integrability. I will review some of them, and present recent results in several quantum systems of interest, including one-dimensional Bose and Fermi gases and spin chains. I will focus in particular on the characterization of the qualitative features of the long-time stationary states which can not be observed at thermal equilibrium, finally presenting some open directions for the field.