We give a pedagogical introduction to the Generalized Hydrodynamic approach
to inhomogeneous quenches in integrable many-body quantum systems. We review
recent applications of the theory, focusing in particular on two classes of
problems: bipartitioning protocols and trap quenches, which represent two
prototypical examples of broken translational symmetry in either the system
initial state or post-quench Hamiltonian. We report on exact results that have
been obtained for generic time-dependent correlation functions and entanglement
evolution, and discuss in detail the range of applicability of the theory.
Finally, we present some open questions and suggest perspectives on possible
future directions.Comment: 46 pages, 13 figures. To appear in JSTAT special issue "Emergent
Hydrodynamics in Integrable Many-body Systems"; v2 minor revision. As appears
in JSTAT special issue "Emergent Hydrodynamics in Integrable Many-body
Systems