Exceptional Generalized Geometry (EGG) is an extension of standard differential geometry such that the U-duality symmetry of string/M theory becomes manifest. It is a step further than Generalized Complex Geometry which geometrizes T-duality. In this work, we aim to write the supersymmetry conditions for compactifications preserving 8 supercharges in a U-duality covariant way. We focus on type IIB compactifications down to five dimensions. We prove that supersymmetry requires integrability conditions on some generalized structures, generalizing the Calabi-Yau conditions (or better the Sasaki-Einstein ones in the five-dimensional case). We comment on concrete applications (future work) in AdS/CFT .