The integrable deformation of string backgrounds has been one of the significant research directions to construct a variety of examples of gauge/gravity duality preserving integrability and to push forward the confirmation of AdS/CFT correspondence. In this introductory talk, I plan to give a basic review of classical integrability of string sigma models with a focus on Lax pairs, to consider the role of the doubled sigma model. [please email a.held@imperial.ac.uk for zoom link or password]