  The original Zee model can easily accommodate a bi-maximal mixing solution
for the atmospheric and solar neutrino problems. From the most recent fit to
the data we obtain a set of parameters for the Zee model. However, the recent
claim on a positive signal observed in a neutrinoless double beta decay, which
requires a nonzero $m_{ee}$, cannot be accounted for by the Zee model. Based on
the observed neutrino mass-square differences and mixings, we derive a few
general patterns for the neutrino mass matrix in the flavor basis, which can
correctly describe the atmospheric, solar, and $0\nu\beta\beta$ data. Finally,
we investigate a few possible extensions to the Zee model, which can give the
required mass patterns.
