Can the gravitation have a mass?

In this essay, we address two long-standing problems of massive gravity: The ghost mode found by Boulware and Deser, and the incompatibility with General Relativity in the massless limit, better known as the vDVZ discontinuity. We present a recent candidate for a ghost-free theory, and show how Einstein's gravity is recovered within a certain macroscopic radius from a mass source, via the Vainshtein mechanism. We also exhibit an exact solution which could account for the late time acceleration of the Universe by means of a small graviton mass.