Progress in two-loop electroweak corrections to gg → HH and gg → gH

In these proceedings, we summarise our recent calculations of next-to-leading order electroweak corrections to Higgs boson pair and Higgs boson plus jet production. The calculations are divided into different regions. In the high-energy region, we analytically calculate the Higgs boson contribution to the leading two-loop Yukawa corrections for gg→HH. These corrections are generated by a single virtual Higgs boson exchange within the top quark loop. Our high-energy expansion yields precise predictions for the region where the Higgs boson transverse momenta p$_T$>120 GeV. In the low-energy region, we compute the complete two-loop electroweak corrections to gg→HH and gg→gH. We obtain analytic results through the large top quark mass expansion, covering all sectors of the Standard Model.