I will give an elementary and informal introduction to an efficient method of solving the Killing spinor equations. The method is based on the description of spinors in terms of forms and can be used to classify the supersymmetric solutions in e.g. 11D and IIB supergravity.

I will review a recently proposed method for solving the Killing spinor equations in arbitrary dimensions. The efficiency of the method will be illustrated by recent progress on the classification of the supersymmetric solutions of 11D and IIB supergravity.