  With the discovery of the Higgs at the LHC, experiments have finally
addressed all aspects of the Standard Model (SM). At this stage, it is
important to understand which windows for beyond the SM (BSM) physics are still
open, and which are instead tightly closed. We address this question by
parametrizing BSM effects with dimension-six operators and performing a global
fit to the SM. We separate operators into different groups constrained at
different levels, and provide independent bounds on their Wilson coefficients
taking into account only the relevant experiments. Our analysis allows to
assert in a model-independent way where BSM effects can appear in Higgs
physics. In particular, we show that deviations from the SM in the differential
distributions of h->Vff are related to other observables, such as triple
gauge-boson couplings, and are then already constrained by present data. On the
contrary, BR(h-> Z+gamma) can still hide large deviations from the SM.
