There has been recent progress towards the solution of the spectral problem for gauge-invariant operators in N=4 Super Yang-Mills, largely driven by the conjectured presence of integrable structures. I will discuss the implications for the perturbative calculation of anomalous dimensions and describe various methods for testing conjectures based on integrability. In particular I will focus on the twist-two operators whose anomalous dimensions can be extracted from the correlator of four energy-momentum multiplets.