In recent years there has been a flurry of interest in so-called 'generalized geometry' (as formalized by Hitchin and his students) motivated by its applications in String Theory. At an algebraic level this kind of generalized geometry arises from exact Courant algebroids.
In this talk I will review some aspects of generalized geometry and discuss more general geometries arising from more general (i.e. non-exact) Courant algebroids, and Leibniz algebroids. I will also give a brief discussion of T-duality in this context.