  In this review we present the octonionic duality for membranes. We start with
a discussion on the relation of the Yang Mills theories and the supermembrane
Hamiltonian in the light-cone gauge. We further derive the self-duality
equations for the membranes and discuss the integrability of the system in 7
and 3 dimensions. Finally, we present classical Euclidean time solutions of
these equations and examine the supersymmetries left intact by the self-duality
equations.
