  The branching fractions of radiative leptonic $\tau$ decays $(\tau \to l \nu
\bar{\nu} \gamma$, $l=e,\mu)$ were recently measured by the Babar collaboration
with a relative error of about 3%. The measurement of the branching ratio
$\mathcal{B} (\tau \to e \bar{\nu} \nu \gamma)$, for a minimum photon energy of
10 MeV in the $\tau$ rest frame, differs from our recent SM prediction by 3.5
standard deviations, whereas our result agrees with Babar's value for
$\mathcal{B} (\tau \to \mu \bar{\nu} \nu \gamma)$. Our predictions also agree
with the measurement of $\mathcal{B} (\mu \to e \bar{\nu} \nu \gamma)$ by the
MEG collaboration. We also report on a recent proposal to test the $\tau$
dipole moments via precise measurements of radiative leptonic $\tau$ decays at
high-luminosity $B$ factories.
