We discuss the matching of NNLO fixed order calculations to parton shower programs in the context of Higgs physics at the LHC. We review different matching methodologies, including the MiNLO and GENEVA approaches, and show results obtained for various Higgs production channels. In the case of GENEVA, we outline the framework and discuss its recent application to the Higgsstrahlung process in which a Higgs is produced in association with a vector boson. We present differential distributions resummed at NNLL$'$ in the beam thrust and matched to the PYTHIA shower and find good agreement with the pure NNLO results for inclusive cases, while the description of other 0-jet-like resummation variables is improved beyond the parton shower approximation.