I will discuss quantum dynamics and transport in systems that are initially split in two halves lying at different temperature or particle density and abruptly connected. After such an inhomogeneous quench, a Non-Equilibrium Steady State (NESS) typically forms in the thermodynamic and large time limit. I will demonstrate how the emergence of NESS can be derived from first principles, starting from non-interacting lattice models in one dimension and considering the effects of different boundary conditions and of interacting defects. Next I will focus on a genuinely interacting integrable system, the Lieb-Liniger gas, for which it has been recently conjectured that Generalised Hydrodynamics (GHD) emerges at large times. I will derive an exact determinant formula for the NESS and show how certain predictions of the above conjecture can be deduced from it.