I will discuss some aspects of the doubled geometry of double field theory. Double field theory provides a reformulation of supergravity with a manifest O(D,D) symmetry, which can be related to the T-duality invariance of string theory on a torus. I will review how one achieves this, by doubling the number of coordinates and introducing a generalised diffeomorphism symmetry. Then, I will discuss how one can characterise the properties of string theory backgrounds viewed as solutions of DFT, and in particular show how to derive the first law of black hole thermodynamics in this framework. Based mainly on 1507.07541 and 1608.04734 (with Alex Arvanitakis).