Late-time cosmic acceleration: ABCD of dark energy and modified theories of gravity

We briefly review the problems and prospects of the standard lore of dark energy. We have shown that scalar fields, in principle, cannot address the cosmological constant problem. Indeed, a fundamental scalar field is faced with a similar problem dubbed naturalness. In order to keep the discussion pedagogical, aimed at a wider audience, we have avoided technical complications in several places and resorted to heuristic arguments based on physical perceptions. We presented underlying ideas of modified theories based upon chameleon mechanism and Vainshtein screening. We have given a lucid illustration of recently investigated ghost-free nonlinear massive gravity. Again, we have sacrificed rigor and confined to the basic ideas that led to the formulation of the theory. The review ends with a brief discussion on the difficulties of the theory applied to cosmology.