Correlation functions and transport coefficients in generalised hydrodynamics

We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. discuss Drude weights, conductivity diffusion constants, as well linear nonlinear response top of equilibrium non-equilibrium states. consider problems from complementary perspectives general hydrodynamic theory many-body systems, including projections, form-factor expansions models, show how they provide a comprehensive consistent set methods to extract scale behaviours. Finally, we overview various applications spin chains field theories.