We update previous analyses of the Zee–Babu model in the light of new data, e.g., the mixing angle θ13, the rare decay μ→eγ and the LHC results. We also analyze the possibility of accommodating the deviations in Γ(H→γγ) hinted by the LHC experiments, and the stability of the scalar potential. We find that neutrino oscillation data and low energy constraints are still compatible with masses of the extra charged scalars accessible to LHC. Moreover, if any of them is discovered, the model can be falsified by combining the information on the singly and doubly charged scalar decay modes with neutrino data. Conversely, if the neutrino spectrum is found to be inverted and the CP phase δ is quite different from π, the masses of the charged scalars will be well outside the LHC reach.