This thesis focuses on modifications on Einstein’s theory of General Relativity, that could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the structure that tells us how to perform derivatives, are studied. These theories appear when imposing that the system must be invariant under the action of the local Poincaré group. Within these theories, the conditions for the appearance of singularities, the movement of fermions, and if it is possible to find different Black Hole solutions than in Einstein’s theory, are studied. Moreover, it is proposed a non-local extension of the mentioned modification, which can make the theory free of instabilities and singularities at the linear limit.