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.