  This present work is based on our previous publications, which all together
trigger our "Killing spinor programme". Other significant spinor fields are
injected into the scheme and the intricate relations between them and their
bilinears are constructed here. The web of relations concerning these
constructions are presented clearly in a Venn diagram. Particular attention is
devoted to the construction of equations satisfied by the homogeneous bilinears
induced from Dirac spinors. Contacts with various physics theories are made
throughout the text and some of the future directions of the programme are
defined.
