I will study the simplest extension of the SM that can account for neutrino masses: the Type-I seesaw. The model introduces a New Physics scale, M, which is often assumed to be much larger than the electroweak scale. However, it is presently unconstrained and the light neutrino masses and mixing can be generated for any value of M above eV. Its determination is one of the most important open questions in neutrino physics. Paying special attention to the contribution of the sterile states to $N_{eff}$ as a function of M, I will show that a large part of the M parameter space can be excluded thanks to cosmological measurements. The implications for neutrinoless double beta decay will also be discussed.