  We review some aspects of the spinorial geometry approach to the
classification of supersymmetric solutions of supergravity theories. In
particular, we explain how spinorial geometry can be used to express the
Killing spinor equations in terms of a linear system for the fluxes and the
geometry of spacetime. The solutions of this linear system express some of the
fluxes in terms of the spacetime geometry and determine the conditions on the
spacetime geometry imposed by supersymmetry. We also present some of the recent
applications like the classification of maximally supersymmetric G-backgrounds
in IIB, this includes the most general pp-wave solution preserving 1/2
supersymmetry, and the classification of N=31 backgrounds in ten and eleven
dimensions.
