Abstract. Integrable models are a class of quantum and classical theories that possess rich symmetries which constrain their dynamics, often leading to their exact solution. Such models also appeared in AdS/CFT, and allowed e.g. to study the spectrum of non-protected operators in planar N=4 super Yang-Mills with stunning precision and efficiency.

Indeed in recent years integrability manifested itself in several AdS/CFT dual pairs, and could be exploited in the computation of a rich set of observables through the bootstrap of appropriate algebraic objects, such as the S-matrix or certain form factors. I would like to outline this integrable bootstrap approach and advocate the opportunity of systematically applying it to a large class of obervables and AdS/CFT duals.

In my talk I will work out a relatively simple example: the computation of the spectrum of AdS3xS3xT4 and AdS3xS3xS3xS1 superstrings in the planar limit. This saw remarkable progress in recent years and is interesting in itself, as these backgrounds are related to the D1-D5 system, to CFT2s with N=(4,4) super-conformal symmetry, and in a certain limit to higher-spin theories. I will then discuss how the approach used there can be adapted to other backgrounds and observables such as three-point functions and one-point functions in presence of defects.

I will conclude by presenting a rich list of open problems that are within our grasp by integrable bootstrap techniques.