The planar $\mathcal{N}=4$ SYM theory and some of its deformations are integrable and should thus be amenable to an explicit solution at finite coupling. This has been achieved for the spectrum of conformal dimensions but the computation of three- or higher-point correlation functions remains a challenge. We will first give a succinct overview of the state-of-the-art integrability techniques, and their limitations, for the computation of correlation functions. We will then present an example of structure constants in the $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM where the hexagonalisation technique allows to reach the exact result. This requires us to derive and compute the (infinite series of) wrapping corrections to the usual hexagon prescription.
