The Gauge/Bethe correspondence is a correspondence between topological gauge theories and quantum integrable systems, discovered by Moore, Nekrasov
and Shatashvili. In this talk, I will review the present status of the Gauge/Bethe correspondence. In particular, I will talk about a Gauge/Bethe
correspondence between the G/G gauged WZW-model and the phase model, and between the G/G gauged WZW-matter model and the q-boson model which is its
one-parameter deformation. This talk is based on arXiv:1209.3800, arXiv:1308.4608 and arXiv:1501.0348.
