The acceleration of the expansion of the Universe which has been identified in recent years has deep connections with some of the most central issues in fundamental physics. At present, the most plausible explanation is some form of vacuum energy. The puzzle of vacuum energy is a central question which lies at the interface between quantum theory and general relativity. Solving it will presumably require to construct a quantum theory of gravity and a correspondingly consistent picture of spacetime. To account for the acceleration of the expansion, one may also think of a more dynamical form of energy, what is known as dark energy, or modifications of gravity. In what follows, we review the the basic models for dark energy and the difficulties encountered in each approach, as well as we discuss the vacuum energy problem.