Integrable 2-dimensional models have numerous applications in theoretical physics, including AdS/CFT. In fact, for certain holographic pairs there is a notion of classical integrability on the worldsheet of the string. In this talk I will use methods to deform the maximally symmetric models and generate backgrounds where some of the global symmetries are broken, still preserving classical integrability. Although I will present some aspects of these deformations for the case of the superstring, most of the discussion will be on how to deform the principal chiral model, where the essential ingredients of the construction appear in simple form.