The discovery of the Higgs boson by the LHC has initiated an era of Higgs precision studies. In the absence of any new particles in the spectrum, and no indication of it at the electroweak scale, suggest that the new physics effects are better explored through precision studies of the interactions of the SM particle spectrum. Related the Higgs sector, this could be investigated efficiently through an effective Lagrangian framework in which the new physics effects are coded through the higher dimensional operators involving Higgs bosons. In the talk, we shall give a brief overview of the studies in the context of LHC as well as future electron collider like ILC/FCC, and present results of our own work in the study of the Higgs self-couplings and Higgs-gauge boson couplings.