The Gauge/Bethe correspondence is a powerful tool for
discovering dualities between supersymmetric field theories and building new
quantum integrable systems. I will illustrate how to quantize spin chain using
4d superconformal QCD, the less familiar Ruijsenaars system using 5d N=2*
theory, and an entirely new Hubbard-Toda model from a coupled 2d-4d system.
Remarkably, the new model reproduces many features of the spectrum of anomalous
dimensions of planar N=4 super Yang-Mills. (based on arXiv:1205.4230 and work
in progress with Nick Dorey)