The current accelerated expansion of the Universe motivates modifying the gravitational laws. Giving a mass to the graviton, thus weakening gravity on large scales, is one such natural modification. However, it turns out to be notoriously difficult to construct such a theory in a consistent way. In this talk, I will review these difficulties as well as the recent breakthroughs that led to the formulation of consistent theories of massive gravity. I will also describe recent personal works about massive gravity around a de Sitter spacetime.