"I will review recent advancements in the development of the Separation of Variables (SoV) program for rational higher rank spin chains, motivated by the recent appearance of SoV-type structures in AdS/CFT. I will discuss the main approaches for constructing a separated variable basis which include diagonalising the B-operator and the action of fused transfer matricies on a suitable vacuum state. I will explain how these approaches are linked and demonstrate how they can be unified into a single framework governed by Yangian representation theory. The outcome is that for any finite-dimensional su(n) spin chain the wave functions (Bethe vectors) factorise into an ascending product of Slater determinants in Baxter Q-functions, allowing us to immediately link this operatorial construction of states with the recently developed functional approach of computing scalar products and form factors." NOTE: this will be an online seminar using Zoom. To participate please fill the registration form on integrability-london.weebly.com.