My talk will be based on joint works with Alfimov, Fateev, Feigin, Hoare and Spodyneiko. I'll try to explain the origin of the duality phenomenon between integrable deformed sigma-models and Toda like QFT's. It relies on the fact that the corresponding integrable structures (actually their UV limits) can be defined as commutants with different types of screening fields of either Wakimoto type (sigma-model type) or exponential type (Toda type). Integrable systems of this class appear as "spin chains" representations for affine Yangian of gl(1) with various "boundary" conditions: periodic for CP(n|m)xU(1) models and fixed for OSP(N|2m) models.
I'll start with brief tour to affine Yangian of gl(1) and its reps. Then I'll review eta-deformed (YB deformed) sigma-models on symmetric spaces and argue that their UV expansion is controlled by Wakimoto type vertex operators. Then on Toda side I'll explain how starting from exponential screening fields find appropriate contact terms which provide the UV completion of the theory and allow to compute perturbative S-matrix for fundamental excitations. The fact that this expansion matches the trigonometric deformation of sigma-model S-matrix (ZZ S-matrix) can be viewed as a non-trivial check of the duality.
As all of this seem to work for O(N) case, its superspace generalization OSP(n|2m) requires some new ideas. Some of them I hope to review as well.