Neutrinos, unlike the other fermions, could be Majorana particles, that is, truly neutral particles identical to their antiparticles. This would have deep consequences in particle physics and cosmology. A unique signature of Majorana neutrinos is the observation of neutrinoless double beta decays (ββ0ν). The discovery of neutrino oscillations — which has shown that neutrinos have masses — and the possible evidence of a ββ0ν signal in the Heildelberg-Moscow experiment have revolutionized the double beta decay comunity. A new generation of experiments with improved sensitivity is currently under design and construction. This paper reviews some of these proposals, with special emphasis in NEXT, that aims at building a 100-kg, high-pressure gas xenon TPC to be hosted in the new Canfranc Underground Laboratory (LSC), in Spain.