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