  We review recent progress in understanding nearly integrable models within
the framework of generalized hydrodynamics (GHD). Integrable systems have
infinitely many conserved quantities and stable quasiparticle excitations: when
integrability is broken, only a few residual conserved quantities survive,
eventually leading to thermalization, chaotic dynamics and conventional
hydrodynamics. In this review, we summarize recent efforts to take into account
small integrability breaking terms, and describe the transition from GHD to
standard hydrodynamics. We discuss the current state of the art, with emphasis
on weakly inhomogeneous potentials, generalized Boltzmann equations and
collision integrals, as well as bound-state recombination effects. We also
identify important open questions for future works.
