  The electromagnetic coupling receives significant contributions to its
running from non-perturbative QCD effects. We present an update of a lattice
QCD study of the Adler function and of its application to the determination of
the running of the QED coupling. We perform a high-statistics computation with
two flavours of O$(a)$ improved Wilson fermions in a large range of momentum
transfer $Q^2$. The running of the electromagnetic coupling, including
contributions from $u$, $d$, $s$ and $c$ valence quarks, is compared to
phenomenological determinations at intermediate $Q^2$ values. An extension of
this study to the determination of the hadronic contributions to the running of
the weak mixing angle is also described.
