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The use of Effective Field Theory (EFT) framework for the characterisation of measurements is becoming prevalent, not just in the conventional realm of low energy observables but also in high energy probes at the LHC. In this talk, we will discuss the role played by the indirect deviations in Higgs couplings for the new non-resonant effects in the quest of new physics. We will investigate the possible signatures of new interactions of the Higgs with the light quarks and the electroweak sector via the VBF and VH production channels in the SMEFT framework and highlight the potential of strongly constraining such new interactions at the HL-LHC and their interpretation. We will also discuss the novel Higgs production in association with a photon at the LHC in the boosted regime. With the implementation of improved search strategies such as multivariate analysis and jet substructure techniques, the distinction of these new physics signals from the background can be optimized to a great extent. Finally, we conclude with the opportunities that the lepton colliders can provide with clean constraints on the nature of Higgs couplings and studies pertaining to the measurement of the Higgs trilinear coupling at the future lepton colliders.