Neutrino oscillations and signals in $\beta$ and $0\nu2\beta$ experiments

Assuming Majorana neutrinos, we infer from oscillation data the expected values of the parameters m_{nu_e} and m_{ee} probed by beta and 0nu2beta-decay experiments. If neutrinos have a `normal hierarchy' we get the 90% CL ranges |m_{ee}| = (0.5 - 5) meV, and discuss in which cases future experiments can test this possibility. For `inverse hierarchy', we get |m_{ee}| = (10 - 57) meV and m_{\nu_e} = (40 - 57) meV. The 0nu2beta data imply that almost degenerate neutrinos are lighter than 0.95 h eV at 90% CL, competitive with the beta-decay bound. We critically reanalyse the data that were recently used to claim an evidence for 0nu2beta, and discuss their implications. Finally, we review the predictions of flavour models for m_{ee} and theta_{13}.