  The hierarchy $\Delta m^2_{atm} \gg \Delta m^2_\odot$ and the large
$\theta_{23}$ mixing angle, as suggested by neutrino oscillation experiments,
can be accounted for by a variety of lepton flavour models. A dichotomy
emerges: i) Models were all neutrino masses are bounded by $m_{atm}\equiv
(\Delta m^2_{atm})^{1/2}\approx 0.03 eV$; ii) Models of quasi-degenerate
neutrinos. It is shown how these different patterns of neutrino masses may
arise from different lepton flavour symmetries. Physical implications are
discussed in the various cases.
