In this talk we will consider the spectrum of anomalous dimensions in N=4 super-Yang-Mills and related theories. We will first discuss the emergence of quantum chaos as one goes from infinite to finite N and how the perturbative spectrum is described by GOE random matrix theory. We will then describe how the integrability of the planar-limit can be used to rewrite the computation of the leading 1/N corrections to the one-loop anomalous dimensions in terms of scalar products of off-shell Bethe states or, alternatively, hexagon-like functions.---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.