In this thesis we present some conceptual and cosmological aspects of two classes of modified gravity models which have been recently proposed with the aim of explaining the observed accelerated expansion in the evolution of our Universe without the need of introducing a cosmological constant term in the gravity action. Explicitly, we illustrate the main features of massive (bi)-gravity and of a class of non-local models of gravity. In the first case the fact that the graviton has a mass is responsible to screen gravitational interactions on length scale of order of the graviton mass and it is this mechanism which give rise to acceleration. In the second case the role of the cosmological constant in driving cosmological acceleration is played by non-local interations in the action for gravity. We illustrate the main results of our work in this field and we discuss a more general framework to which our results belong.