  We discuss the main features of quantum integrable models taking the classes
of universality of the Ising model and the repulsive Lieb-Liniger model as
paradigmatic examples. We address the breaking of integrability by means of two
approaches, the Form Factor Perturbation Theory and semiclassical methods. Each
of them has its own advantage. Using the first approach, one can relate the
confinement phenomena of topological excitations to the semi-locality of the
operator which breaks integrability. Using the second approach, one can control
the bound states which arise in each phase of the theory and predict that their
number cannot be more than two.
