  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.
