It is often suggested that integrable 2d sigma models should be renormalizable, however this relationship has only previously been checked in the 1-loop approximation. The aim of this work is to understand what happens beyond 1-loop. We shall pedagogically introduce the lambda- and eta-models, and non-abelian duality. Based on these examples, we confirm that classically integrable sigma models appear to be 2-loop renormalizable if supplemented with a particular choice of finite counterterms, i.e. quantum corrections to the target space geometry. The 2-loop beta-function of the lambda-model is computed, matching the known results for groups and symmetric spaces in the limit when the lambda-model becomes the corresponding non-abelian dual model. This leads to the statement that non-abelian duality commutes with the RG flow beyond 1-loop order. NOTE: Please register to the mailing list at integrability-london.weebly.com to receive the link for the Zoom meeting.