  The time evolution of the entanglement entropy in non-equilibrium quantum
systems provides crucial information about the structure of the time-dependent
state. For quantum quench protocols, by combining a quasiparticle picture for
the entanglement spreading with the exact knowledge of the stationary state
provided by Bethe ansatz, it is possible to obtain an exact and analytic
description of the evolution of the entanglement entropy. Here we discuss the
application of these ideas to several integrable models. First we show that for
non-interacting systems, both bosonic and fermionic, the exact time-dependence
of the entanglement entropy can be derived by elementary techniques and without
solving the dynamics. We then provide exact results for interacting spin chains
that are carefully tested against numerical simulations. Finally, we apply this
method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in
the attractive and repulsive regimes. We highlight a peculiar behaviour of the
entanglement entropy due to the absence of a maximum velocity of excitations.
