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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.