Appears in collection : Guido Festuccia - Curved-space supersymmetry

We discuss aspects of supersymmetry on curved-space, with an emphasis on 4d N= 1 theories. Topics include supercurrents, rigid supergravity, curved superspace (for S4 and S3×R), a classification of 4d N= 1 supersymmetric backgrounds and the dependence of supersymmetric observables on the background geometry. Some of these topics are also described for 3d N= 2 and 4d N= 2 supersymmetries.