Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms

The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article we provide an introductory survey of the impact of Yang-Baxter integrable models on experiments in condensed matter physics and ultracold atoms. A number of prominent examples are covered, including the hard-hexagon model, the Heisenberg spin chain, the transverse quantum Ising chain, a spin ladder model, the Lieb-Liniger Bose gas, the Gaudin-Yang Fermi gas and the two-site Bose-Hubbard model. The review concludes by pointing to some other recent developments with promise for further progress.