A unique linear theory describing a free massive spin-2 representation of the Poincare group - Fierz-Pauli model - has proven to be extremely hard to generalize at the nonlinear level, without violating its consistency. Recently, a class of four-dimensional, ghost-free non-linear extensions of the FP theory has been constructed, which are natural candidates for describing massive gravity. After reviewing some formal aspects of these theories as well as their immediate extensions, I will discuss their relevance for cosmology.