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