Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. After a general introduction on some aspects of extended (super)gravity theories in four dimensions and the structure of their U-orbits, I will consider their U-duality Lie groups "of type E7", and the corresponding notion of Freudenthal duality. I will also elucidate and comment on the relation between the Hessian of the black hole entropy and the pseudo-Riemannian, rigid special Kaehler metric of the pre-homogeneous vector spaces associated to the U-orbits.
