  We revisit rare radiative leptonic decays $B_{s,d}\to \gamma e^+e^-$ and
$B_{s,d}\to \gamma \mu^+\mu^-$ in the Standard Model and provide the updated
estimates for various differential distributions (the branching ratios, the
forward-backward asymmetry, and $R_{\mu/e}$, the ratio of the differential
distribution for muons over electrons in the final state). The new ingredients
of this work compared to the existing theoretical analyses are the following:
(i) we calculate all $B_d\to\gamma$ and $B_s\to\gamma$ form factors induced by
the vector, axial-vector, tensor and pseudotensor quark currents within the
relativistic dispersion approach based on the constituent quark picture; (ii)
we perform a detailed analysis of the charm-loop contributions to radiative
leptonic decays: we obtain constraints imposed by the electromagnetic gauge
invariance and discuss the existing ambiguities in the charmonia contributions.
