Precise predictions for $\mathrm{WH}$+jet production at the LHC

We present precise predictions for the production of a Higgs boson in association with a hadronic jet and a W boson at hadron colliders. The behaviour of QCD corrections are studied for fiducial cross sections and distributions of the charged gauge boson and jet-related observables. The inclusive process (at least one resolved jet) and the exclusive process (exactly one resolved jet) are contrasted and discussed. The inclusion of QCD corrections up to O(αs3) leads to a clear stabilisation of the predictions and contributes substantially to a reduction of remaining theoretical uncertainties.