  We present NLO electroweak corrections to Higgs production in association
with off-shell top-antitop quark pairs. The full process
$\text{p}\text{p}\to\text{e}^+\nu_{\text{e}}
\mu^-\bar{\nu}_\mu\text{b}\bar{\text{b}} \text{H}$ is considered, and hence all
interference, off-shell, and non-resonant contributions are taken into account.
The electroweak corrections turn out to be below one per cent for the
integrated cross section but can exceed $10\%$ in certain phase-space regions.
In addition to its phenomenological relevance, the computation constitutes a
major technical achievement as the full NLO virtual corrections involving up to
9-point functions have been computed exactly. The results of the full
computation are supported by two calculations in the double-pole approximation.
These also allow to infer the effect of off-shell contributions and emphasise
their importance especially for the run II of the LHC. Finally, we present
combined predictions featuring both NLO electroweak and QCD corrections in a
common set-up that will help the experimental collaborations in their quest of
precisely measuring the aforementioned process.
