  We analyze the viability of the Zee-Babu model as an explanation of observed
neutrino masses and mixings and the possibility that the model is confirmed or
discarded in experiments planned for the very close future. The allowed
parameter space is studied analytically by using some approximations and
partial data. Then, a complete scanning of all parameters and constraints is
performed numerically by using Monte Carlo methods. The cleanest signal of the
model will be the detection of the doubly charged scalar at the LHC and its
correlation with measurements of the branching ratio of $\mu\to e\gamma$ at the
MEG experiment. In addition, the model offers interesting predictions for
$\tau^{-}\to\mu^{+}\mu^{-}\mu^{-}$ experiments, lepton-hadron universality
tests, the $\theta_{13}$ mixing in neutrino oscillations and the
$<m_{\nu}>_{ee}$ parameter of neutrinoless double beta decay.
