U-duality covariant approach to string and M-theory

M-theory on a $d$-torus is known to possess U-duality symmetry given by exceptional groups $E_d$ (for supergravity known as Cremmer-Julia symmetry). In the talk I will review the construction of exceptional field theory that regards U-duality as a particular case of symmetries of some underlying extended space. In particular, I will cover dimensional reductions of such theories, their relations with (maximal) gauged supergravities and embedding tensor formalism, as well as applications to description of exotic branes, non-geometry and deformations of sigma-model backgrounds.