  In the framework of nonrelativistic QCD, we study the radiative decays of
bottomonia into charmonia, including $\Upsilon\to \chi_{cJ}\gamma$,
$\Upsilon\to \eta_c\gamma$, $\eta_b\to J/\psi\gamma$, and $\chi_{bJ}\to
J/\psi\gamma$. We give predictions for their branching ratios with numerical
calculations. E.g., we predict the branching ratio for $\eta_b\to J/\psi\gamma$
is about $1\times 10^{-7}$. As a phenomenological model study, we further
extend our calculation to the radiative decays of bottomonia into light mesons
by assuming the $f_2(1270)$, $f_2'(1525)$ and other light mesons to be
described by nonrelativistic $q\bar q ~(q=u,d,s)$ bound states with constituent
quark masses. The calculated branching ratios for $\Upsilon\to f_2(1270)\gamma$
and $\Upsilon\to f_2'(1525)\gamma$ are roughly consistent with the CLEO data.
Comparisons with radiative decays of charmonium into light mesons such as
$J/\psi\to f_2(1270)\gamma$ are also given. In all calculations the QED
contributions are taken into account and found to be significant in some
processes.
