The Galileon model introduced by Nicolis et al. is an extension of the
decoupling limit of DGP, involving a relativistic scalar pi with specific
derivative self-interactions. I will show how this model naturally arises in
some limit of braneworld scenarios as well as in four-dimensional massive
gravity, where the scalar pi plays the role of the helicity-0 mode of the
graviton. I will then discuss some applications for early cosmology in a
model of Galileon Inflation, as well as for late cosmology mentioning the
implications for the late-time acceleration of the Universe.
