  We compute three-loop vertex corrections to $b\to s\gamma$ induced by
current-current operators. The results are presented as expansions in $m_c/m_b$
with numerical coefficients which allow to cover all relevant values for the
heavy quark masses in different renormalization schemes. Moreover we provide
for the first time analytic results for the next-to-leading order contribution.
Our results present an important building block to the next-to-next-to-leading
order interference contributions of the current-current operators $Q_1$ and
$Q_2$ with the electric dipole operator $Q_7$.
