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In order to explain the Late-times accelerated expansion of the Universe wemust appeal to some form of Dark Energy. In the standard model of cosmology,the latter is interpreted as a Cosmological Constant $\Lambda$. However, for anumber of reasons, a Cosmological Constant is not completely satisfactory. Inthis thesis we study Dark Energy models of geometrical nature, and thus amanifestation of the underlying gravitational theory. In the first part of thethesis we will review the $\Lambda$CDM model and give a brief classification ofthe landscape of alternative Dark Energy candidates based on the Lovelocktheorem. The second part of the thesis is instead devoted to the presentationof our main results on the topic of Dark Energy. To begin with, we will reportour studies about nonlocal modifications of gravity involving the differentialoperator $\Box^{-1}R$, with emphasis on a specific model and on the commonbehavior shared by this and similar theories in the late stages of theevolution of the Universe. Then we introduce a novel class of modified gravitytheories based on the anticurvature tensor $A^{\mu\nu}$ (the inverse of theRicci tensor), and assess their capability as source of Dark Energy. Finally,we will discuss a type of drift effects which we predicted in the contest ofStrong Gravitational Lensing, which could be employed both to study theeffective equation of state of the Universe and to constrain violations of theEquivalence Principle.

Accelerated expansion as manifestation of gravity: when Dark Energy belongs to the left