The production of a Higgs boson at the LHC suffers from large higher order corrections. This is true also when it is accompanied by further jets. The most precise results rely on computations in an effective theory where the heavy quark loops, mediating the coupling between the Higgs boson and the gluons, are integrated out. As the LHC is delivering more and more precise data, it is important to understand in detail the validity range of such effective theory predictions, in particular in view of boosted analyses. In this talk we will present detailed comparisons between effective theory results and predictions obtained in the full theory.