One of the most challenging problems in theoretical physics today is the so called cosmological constant problem. While current observational constraints are consistent with the predictions of GR with a tiny cosmological constant, often referred to as the dark energy, it remains possible that it\'s the deviation of the law of gravity at large distance from Einstein\'s theory that resolves the puzzle. In this talk, I will briefly review some of the theoretical attempts made along this line, including the simple massive gravity, large extra dimensions, Unimodular gravity, classically constrained gravity, as well as their difficulties. I will then focus on some most recent study on the theory of massive graviton in de Sitter space, which may be more closely related to the reality both today and during the inflationary epoch. In particular, I would describe a model, in which one is able to open up the forbidden mass range of the graviton on a de Sitter background discovered by Higuchi.