In this talk, I am going to review some aspects of the current state of the art of Integrability in the AdS/CFT correspondence and beyond. I will first describe a general nonperturbative approach to compute correlation functions of local operators in the N=4 Supersymmetric Yang-Mills theory which allows us to explore the theory even beyond the most well studied planar limit. In the second part, I will describe my recent work on the study of N=4 Supersymmetric Yang-Mills on RP^4. This provides a new solvable set up of AdS/CFT that allows for the exact computation of new observables using integrability, localization and holography.
https://indico.math.cnrs.fr/event/7679/