Recent results from the Large Hadron Collider (LHC) has proved the existence of the
long-awaited Higgs boson in the Standard Model (SM). Results based on the 8 TeV LHC data show that
the properties of this boson are more-or-less consistent with the SM expectations. Whether it has
the exact same nature as the SM Higgs or whether there is any scope for departure from the SM
is an important question. In this talk, I shall discuss the coupling modifications of the Higgs boson
in two model-independent approaches, viz., by simple rescaling of the SM couplings and by
introducing new Lorentz structures in the Lagrangian. Dimension-6 (6D) operators, introducing such
momentum-dependent vertices will be presented and bounds on their coefficients from the recent
LHC data will be discussed. I shall show that considering the effects of the 6D operators on the
experimental cut-efficiencies might become important in exploring such couplings. Various kinematic
variables probing such couplings will be looked at, critically. Finally, the possibility to see the
effects of such modified couplings at a future e+e- collider (Higgs factory) will be discussed.