Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was originally introduced in four-dimensional Maxwell-Einstein theories coupled to non-linear sigma models of scalar fields. After a general introduction on some aspects of extended (super)gravity theories 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 elucidate and comment on the relation between the Hessian of the black hole entropy and the pseudo-Riemannian, rigid, para-special Kaehler metric of the pre-homogeneous vector spaces associated to the U-orbits. I will conclude with some hints for further future developments.