The idea of degravitation is to tackle the cosmological constant problem by modifying gravity at large distances such that a large cosmological constant does not backreact as much as anticipated from standard General Relativity. After reviewing the fundamental aspects of degravitation, I will present a new class of theories of massive gravity capable of exihibiting the degravitation behaviour. I will then comment on the stability of such models and show in the decoupling limit how theories of gravity with at least two additional helicity-0 excitations can provide a stable realization of degravitation.