**Summary:** The paper explores the theoretical aspects of massive gravity, focusing on the challenges and progress in modifying general relativity to give the graviton a mass. It begins by discussing the nature of general relativity as a massless spin-2 theory and the motivation for modifying it, including the cosmological constant problem and the need for a self-accelerating universe. The paper reviews the history of massive gravity, highlighting key concepts such as the vDVZ discontinuity and the Boulware-Deser ghost. It then presents the Fierz-Pauli action for a free massive graviton, showing that it describes a massive spin-2 particle with five degrees of freedom. The paper discusses the linear and nonlinear responses of massive gravity to sources, the Stückelberg trick for restoring gauge invariance, and the Vainshtein mechanism for screening nonlinear effects. It also reviews recent developments, including the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the emergence of massive gravitons from extra dimensions and brane worlds. The paper concludes with a discussion of the theoretical implications and future directions for massive gravity research.**Summary:** The paper explores the theoretical aspects of massive gravity, focusing on the challenges and progress in modifying general relativity to give the graviton a mass. It begins by discussing the nature of general relativity as a massless spin-2 theory and the motivation for modifying it, including the cosmological constant problem and the need for a self-accelerating universe. The paper reviews the history of massive gravity, highlighting key concepts such as the vDVZ discontinuity and the Boulware-Deser ghost. It then presents the Fierz-Pauli action for a free massive graviton, showing that it describes a massive spin-2 particle with five degrees of freedom. The paper discusses the linear and nonlinear responses of massive gravity to sources, the Stückelberg trick for restoring gauge invariance, and the Vainshtein mechanism for screening nonlinear effects. It also reviews recent developments, including the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the emergence of massive gravitons from extra dimensions and brane worlds. The paper concludes with a discussion of the theoretical implications and future directions for massive gravity research.