In the last decades, integrability became a powerful tool to exploit dualities between strongly coupled gauge theories and string theories, and it is at the heart of recent progress for the AdS/CFT correspondence. The spectral problem of the planar N=4 SYM theory was reduced to a Riemann-Hilbert problem, drawing inspiration from the Thermodynamic Bethe Ansatz approach for spin chains and integrable 2d theories. Amplitudes and correlation functions also benefit from this approach, and specific methods based on the so-called form factor expansion were successfully applied to obtain systematic expansions at weak and strong coupling, and in some cases all-loop results. The talk will review the hexagonalization method and some recent results for correlation functions in N=4 SYM and in the related cyclic Z_K quiver theories.