In this talk I will describe recent progress towards understanding integrable deformations of superstrings in AdS backgrounds. One well-known example of such a deformation is the TsT transformation, which involves a T-duality, a shift introducing the deformation parameter, and a reverse T-duality. After introducing this deformation, I will give two alternative constructions: (i) as a particular non-abelian duality, and (ii) as a particular Yang-Baxter deformation. In the second part of the talk I will outline how this extends to a general relationship between non-abelian duality and Yang-Baxter deformations, and discuss the consequences for the Weyl invariance of the deformed models.