  The role of Killing and Killing-Yano tensors for studying the geodesic motion
of the particle and the superparticle in a curved background is reviewed.
Additionally the Papadopoulos list [74] for Killing-Yano tensors in G
structures is reproduced by studying the torsion types these structures admit.
The Papadopoulos list deals with groups G appearing in the Berger
classification, and we enlarge the list by considering additional G structures
which are not of the Berger type. Possible applications of these results in the
study of supersymmetric particle actions and in the AdS/CFT correspondence are
outlined.
