The present thesis explores the theoretical and phenomenological aspects of theories of massive gravity in three and four spacetime dimensions.

We start with investigating cosmology of a recently proposed class of four-dimensional nonlinear covariant extensions of Fierz-Pauli massive gravity. We begin with a short-distance, "decoupling" limit of the theory, describing the local dynamics of the universe. In this limit, the theory is a scalar-tensor model of a unique form defined by symmetries. We find that it admits a self-accelerated solution, with the Hubble parameter set by the graviton mass. The negative pressure causing the acceleration is due to a condensate of the helicity-0 component of the massive graviton, and the background evolution, in the approximation used, is indistinguishable from the ΛCDM model. Fluctuations about the self-accelerated background are stable for a certain range of parameters involved. Most surprisingly, the fluctuation of the helicity-0 field decouples from an arbitrary source in the linearized theory, hiding the associated fifth force from any observer on this background.

The local similarity with the ΛCDM model however can not carry through beyond the horizon. The very same constraint, that eliminates the ghost, does not allow for truly homogeneous and isotropic FRW cosmologies in this class of theories. Nevertheless, at matter/radiation energy densities above a certain crossover value, these solutions follow the standard FRW evolution with a great accuracy, while the inhomogeneities become more and more pronounced as the density drops, and below the crossover value the evolution significantly departs from that of FRW.

In the second part of the thesis, we explore the nonlinear classical dynamics of the three-dimensional theory of “New Massive Gravity”. We find that the theory passes remarkably highly nontrivial consistency checks at the nonlinear level. We give a non-perturbative argument based on the presence of additional symmetries that the full theory does not lead to any extra degrees of freedom, suggesting that a 3D analog of the 4D Boulware-Deser ghost is not present in this theory. Last but not least, we generalize “New Massive Gravity” and construct a class of 3D cubic order massive models that retain the above properties.