Integrable lattice models in 1+1 dimensions have been a topic of much fascination in physics since the early days of quantum mechanics. Recently, a work by Costello has offered a new perspective in which these models are understood in terms of a 4D topological gauge theory. An interesting aspect of this proposal is the close connection with 3D Chern-Simons theory and knot invariants. I will explain how to motivate the 4D topological theory using string dualities and higher dimensional gauge theories. I will also describe how this construction shares som features with the derivation of knot homology from gauge theory proposed by Witten.