Considerable progress has taken place in recent years in modeling the large-scale dynam- ics of one-dimensional quantum many-body systems that are integrable or nearly inte- grable, thanks to the advent of Generalized Hydrodynamics. In particular, Generalized Hydrodynamics provides a computationally efficient tool for simulating experiments on one-dimensional Bose gases. In this habilitation thesis I review the main results I ob- tained with my co-authors, both on theory developments and on the application to cold atom experiments. I also discuss our recent attempts at describing the effects of quantum fluctuations of out-of-equilibrium quantum gases within that framework.I also present a few results on other topics in low-dimensional quantum many-body physics. These include basic results on ‘operator entanglement’, an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators in one- dimensional quantum systems, as well as results on two-dimensional chiral topological phases (e.g. quantum Hall states, Chern bands, or p+ip superfluids) from the point of view of their entanglement properties.