O( d,d) covariant formulation of Type II supergravity and Scherk-Schwarz reduction

T-duality is a stringy symmetry which relates string backgrounds with different space-time geometries. In the low energy limit, it manifests itself as a continuous O(d,d) symmetry acting on supergravity fields, after dimensional reduction on a d dimensional torus. Double Field Theory (DFT) is a T-duality covariant extension of string theory which aims to realize O(d,d) as a manifest symmetry for the low energy effective space-time actions of string theory without dimensional reduction. The mathematical framework needed to construct DFT goes beyond Riemannian geometry and is related to Hitchin's generalized geometry program. On the other hand, Scherk-Schwarz reduction of DFT of Type II strings with a duality twist in O(d,d) yields Gauged Double Field Theory (GDFT), that can be regarded as an O(d,d) covariant extension of gauged supergravity. The purpose of this contribution is to give a short review on Scherk-Schwarz reductions of DFT and its intriguing connections to integrable deformations of string sigma models.