Cosmological surveys are at the verge of detecting neutrino masses for the first time ever. This highly anticipated measurement will set a clear target for terrestrial experiments aimed at measuring the neutrino mass scale via beta decay, many of which rely on work conducted at CENPA. I start the talk with a summary of the different ways in which cosmology is sensitive to neutrino masses, and the observables we will use to measure the neutrino mass scale in the upcoming decade. The success of this program relies on our ability to efficiently compute known observables, and I discuss the recent development of an accurate fluid approximation to study the evolution of massive neutrino perturbations, with the goal of speeding up standard cosmological inference techniques. I also advocate for new signatures of neutrino masses in the large scale structure, which can strengthen the case for a future cosmological measurement of the neutrino mass scale. An exciting possibility is given by neutrino wakes effects, wherein massive neutrinos preferentially accumulate downstream of moving cold dark matter structures.