This review by Claudia de Rham provides an overview of recent progress in massive gravity, a theory that modifies general relativity by introducing a non-zero mass for the graviton. The paper begins by discussing how different theories of massive gravity emerge from higher-dimensional theories of general relativity, leading to models such as the Dvali–Gabadadze–Porrati (DGP) model, cascading gravity, and ghost-free massive gravity. It explores the theoretical and phenomenological consistency of these models, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and cosmological solutions. The review also presents alternative and related models of massive gravity, including new massive gravity, Lorentz-violating massive gravity, and non-local massive gravity. The paper concludes with a discussion of the phenomenological aspects of ghost-free massive gravity, such as gravitational waves, solar system tests, lensing, pulsars, black holes, and cosmology.This review by Claudia de Rham provides an overview of recent progress in massive gravity, a theory that modifies general relativity by introducing a non-zero mass for the graviton. The paper begins by discussing how different theories of massive gravity emerge from higher-dimensional theories of general relativity, leading to models such as the Dvali–Gabadadze–Porrati (DGP) model, cascading gravity, and ghost-free massive gravity. It explores the theoretical and phenomenological consistency of these models, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and cosmological solutions. The review also presents alternative and related models of massive gravity, including new massive gravity, Lorentz-violating massive gravity, and non-local massive gravity. The paper concludes with a discussion of the phenomenological aspects of ghost-free massive gravity, such as gravitational waves, solar system tests, lensing, pulsars, black holes, and cosmology.