Division algebras, extended supersymmetries and applications

I present here some new results which make explicit the role of the divisio n algebras R, C, H, O in the construction and classification of, respective ly, N = 1, 2, 4, 8 global supersymmetric quantum mechanical and classical d ynamical systems. In particular an N = 8 Malcev superaffine algebra is intr oduced and its relation to the non-associative N = 8 SCA is discussed. A li st of present and possible future applications is given.