Classification of supersymmetric backgrounds of string theory

We review the recent progress made towards the classification of supersymmetric solutions in ten and eleven dimensions with emphasis on those of IIB supergravity. In particular, the spinorial geometry method is outlined and adapted to nearly maximally supersymmetric backgrounds.We then demonstrate its effectiveness by classifying the maximally supersymmetric IIB G-backgrounds and by showing that N = 31 IIB solutions do not exist