The h -> V+F amplitude, where V=W, Z, and F is a generic leptonic or hadronic final state, can be decomposed in terms of a limited set of form factors. I discuss such general decomposition; how these form factors can be accessed experimentally in h -> Zl+l- decays and in the h+V associated production; why the form factors carries additional information on physics beyond the SM with respect to the "standard" signal-strength analyses. The interest in this perspective of searching for the rare decay modes h -> VP, where P is a single light hadron is also briefly discussed.