We review the non-equilibrium dynamics of many-body quantum systems after a\nquantum quench with spatial inhomogeneities, either in the Hamiltonian or in\nthe initial state. We focus on integrable and many-body localized systems that\nfail to self-thermalize in isolation and for which the standard hydrodynamical\npicture breaks down. The emphasis is on universal dynamics, non-equilibrium\nsteady states and new dynamical phases of matter, and on phase transitions far\nfrom thermal equilibrium. We describe how the infinite number of conservation\nlaws of integrable and many-body localized systems lead to complex\nnon-equilibrium states beyond the traditional dogma of statistical mechanics.\n
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