A possible connection between the hints for lepton flavour non-universality in the $B$-decay observables $R_{K^{(*)}}$ and $R_{D^{(*)}}$ and radiative models for Majorana neutrino mass generation is discussed. After a brief survey of the anomalies, a systematic approach to radiative Majorana-mass model building using $\Delta L = 2$ effective operators constructed out of standard model fields is reviewed. Then two specific models are examined: a minimal model containing the $S_1 \sim (3,1,-1/3)$ scalar leptoquark, and a next-to-minimal model containing $S_1$ and $S_3 \sim (3,3,-1/3)$.