This doctoral thesis encompasses a detail study of phenomenological as well as theoretical consequences derived from the existence of a graviton mass within the ghost-free theory of massive gravity, the de Rham-Gabadadze-Tolley (dRGT) theory, which incorporates a 2-parameter family of potentials. In this thesis we pursue to test the physical viability of the theory. To start with, we have put constraints on the parameters of the theory in the decoupling limit based on purely theoretical grounds, like classical stability in the cosmological evolution. Hereby, we were able to construct self- accelerating solutions which yield similar cosmological evolution to a cosmological constant. Furthermore we studied the degravitating solutions, which enables us to screen an arbitrarily large cosmological constant in the decoupling limit. Nevertheless, conflicts with observations pushes the allowed value of the vacuum energy to a very low value rendering the found degravitating solution phenomenologically not viable for tackling the old cosmological constant problem. Next, we constructed a proxy theory to massive gravity from the decoupling limit resulting in non-minimally coupled scalar-tensor interactions as an example of a subclass of Horndeski theories. We explored the self-accelerating and degravitating solutions in this proxy theory in analogy to the decoupling limit and extended the analysis by studying the change in the linear structure formation. Furthermore, Galileon models are a class of effective field theories that naturally arise in the decoupling limit of theories of massive gravity. We show that the existence of superluminal propagating solutions for multi-galileon theories is an unavoidable feature. Finally, we addressed the natural question of whether the introduced parameters in the theory are subject to strong renormalization by quantum loops. Starting with the decoupling limit we have shown how the non-renormalization theorem protects the graviton mass from quantum corrections. Beyond the decoupling limit the quantum corrections are proportional to the graviton mass, proving its technical naturalness in an explicit realization of 't Hooft's naturalness argument. Moreover, we pushed the analysis beyond the decoupling limit by studying the stability of the graviton potential when including matter and graviton loops. One-loop matter corrections contribute a cosmological constant term leaving the potential unaffected. On the contrary, the one-loop contributions from the gravitons destabilize the special structure of the potential. Nevertheless, we showed that even in the case of large background configuration, the Vainshtein mechanism redresses the one-loop effective action so that the detuning remains irrelevant below the Planck scale.