Galileons in the sky

We review the different frameworks in which Galileon scalar fields have been seen to emerge such as in DGP, New Massive Gravity and Ghost-free Massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models. The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. In particular, we review the self-accelerating and degravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology.